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+{
+    "url": "http://arxiv.org/abs/2405.05330v1",
+    "title": "Chemo-dynamical Evolution of Simulated Satellites for a Milky Way-like Galaxy",
+    "abstract": "The chemical abundances of Milky Way's satellites reflect their star\nformation histories (SFHs), yet, due to the difficulty of determining the ages\nof old stars, the SFHs of most satellites are poorly measured. Ongoing and\nupcoming surveys will obtain around ten times more medium-resolution spectra\nfor stars in satellites than are currently available. To correctly extract SFHs\nfrom large samples of chemical abundances, the relationship between chemical\nabundances and SFHs needs to be clarified. Here, we perform a high-resolution\ncosmological zoom-in simulation of a Milky Way-like galaxy with detailed models\nof star formation, supernova feedback, and metal diffusion. We quantify SFHs,\nmetallicity distribution functions, and the $\\alpha$-element (Mg, Ca, and Si)\nabundances in satellites of the host galaxy. We find that star formation in\nmost simulated satellites is quenched before infalling to their host. Star\nformation episodes in simulated satellites are separated by a few hundred Myr\nowing to supernova feedback; each star formation event produces groups of stars\nwith similar [$\\alpha$/Fe] and [Fe/H]. We then perform a mock observation of\nthe upcoming Subaru Prime Focus Spectrograph (PFS) observations. We find that\nSubaru PFS will be able to detect distinct groups of stars in [$\\alpha$/Fe] vs.\n[Fe/H] space, produced by episodic star formation. This result means that\nepisodic SFHs can be estimated from the chemical abundances of $\\gtrsim$ 1,000\nstars determined with medium-resolution spectroscopy.",
+    "authors": "Yutaka Hirai, Evan N. Kirby, Masashi Chiba, Kohei Hayashi, Borja Anguiano, Takayuki R. Saitoh, Miho N. Ishigaki, Timothy C. Beers",
+    "published": "2024-05-08",
+    "updated": "2024-05-08",
+    "primary_cat": "astro-ph.GA",
+    "cats": [
+        "astro-ph.GA",
+        "astro-ph.HE",
+        "astro-ph.IM",
+        "astro-ph.SR"
+    ],
+    "label": "Original Paper",
+    "paper_cat": "Diffusion AND Model",
+    "gt": "1.",
+    "main_content": "\u2217JSPS Research Fellow stellar masses (M\u2217) less than \u2248109 M\u2299are typically categorized as dwarf galaxies. Among them, gas-free dwarf galaxies with M\u2217\u2273105 M\u2299are called classical dwarf spheroidal galaxies (dSphs), while those with M\u2217\u2272105 M\u2299are identified as ultrafaint dwarf galaxies (UFDs). Many of the dwarf galaxies in the Local Group are satellites of the MW or M31; interactions with their more massive hosts could affect the chemodynamical properties of these satellites (Genina et al. 2019; Kvasova et al. 2024). Satellites exhibit a wide variety of star formation histories (SFHs) and chemical abundances. The SFHs of Local Group dwarf galaxies can be derived by colormagnitude diagrams (CMDs, e.g., de Boer et al. 2012a,b; Weisz et al. 2014; Ren et al. 2024). Weisz et al. (2014) comprehensively studied SFHs in the Local Group dwarf arXiv:2405.05330v1  [astro-ph.GA]  8 May 2024 2 Hirai et al. galaxies. They found that more massive systems tend to have more extended SFHs. They also showed that MW or M31 satellites have a shorter duration of star formation than those in the field populations. Chemical abundances reflect the SFHs and nucleosynthesis pathways in satellites (e.g., Tolstoy et al. 2009; Kirby et al. 2010, 2011a,b; Ishigaki et al. 2014; Hill et al. 2019; Sk\u00b4 ulad\u00b4 ottir et al. 2024). Kirby et al. (2011b) analyzed metallicity distribution functions (MDFs) of the MW\u2019s satellites with Keck/DEIMOS with a chemical evolution model. They found that the MDFs of more-luminous systems are well-fit with their Extra Gas Model, which assumes gas infall. However, their best-fit effective yields suggested that gas outflow also played an important role in the chemical evolution of less-luminous systems. Thanks to the difference in the delay times between core-collapse supernovae (CCSNe) and type Ia supernovae (SNe Ia), the ratios of \u03b1-elements (e.g., Mg, Ca, and Si) to Fe are often used as an indicator for the rate of chemical evolution. For example, Hill et al. (2019) reported high-resolution spectroscopy of 99 stars in the Sculptor dSph. They found that the decreasing trend of [\u03b1/Fe]1 toward higher metallicity starts at [Fe/H] = \u22121.8. This metallicity is lower than the start of this trend in the MW, indicating that the chemical evolution of Sculptor dSph proceeded more slowly. Numerical simulations have been performed to understand the SFHs and chemical evolution of dwarf galaxies (e.g., Revaz et al. 2009; Okamoto et al. 2010; Revaz & Jablonka 2012, 2018; Hirai et al. 2015, 2017, 2018, 2019; Jeon et al. 2017; Escala et al. 2018; Simpson et al. 2018; Garrison-Kimmel et al. 2019; Applebaum et al. 2021; Di Cintio et al. 2021; Samuel et al. 2022; Rodr\u00b4 \u0131guez et al. 2022). Di Cintio et al. (2021) found that 25% of their simulated satellite dwarf galaxies exhibit an enhancement of star formation after infall to their host. In contrast, the star formation in satellites with little gas or small pericentric distances is quenched after infall due to ram pressure stripping. Escala et al. (2018) introduced the process of metal diffusion in cosmological zoom-in simulations of the Feedback in Realistic Environment (FIRE) project (Hopkins et al. 2014), and analyzed chemical abundances in their simulated dwarf galaxies. They found that the MDFs and intrinsic scatter in [\u03b1/Fe] are similar in satellite and isolated dwarf galaxies, suggesting that internal chemical evo1 [X/Y] = =log(NX/NY) \u2212log(NX/NY)\u2299, where NX and NY are the number densities of elements X and Y, respectively. lution plays a more important role than environmental effects. Ongoing and upcoming surveys will significantly enlarge the number of stars in satellites of the MW with available spectroscopy (e.g., Takada et al. 2014; Cooper et al. 2023; Jin et al. 2023). For example, the Dark Energy Spectroscopic Instrument (DESI) Milky Way Survey will observe 7 million stars with magnitudes 16 < r < 20 at Galactic latitudes |b| > 20\u25e6(Cooper et al. 2023). Their footprint includes 31 Local Group dwarf galaxies. This potentially could yield medium-resolution (R \u223c5, 000) spectroscopy of the member stars in some of these galaxies from their centers to their outskirts. The upcoming Subaru Prime Focus Spectrograph (PFS) will target 7 Local Group dwarf galaxies in their Galactic Archaeology survey (Takada et al. 2014). Thanks to their wide field of view (1.25 square degrees) and massively multiplexed spectroscopic capability (2,394 fibers), they can obtain medium-resolution (R \u223c5, 000) spectroscopy for stars with magnitudes g \u227223 in these galaxies. The Subaru PFS will yield radial velocities, [Fe/H], carbon, \u03b1-elements, and nickel abundance measurements in each galaxy for \u22481,000 to 14,000 stars, more than ten times larger than the current numbers of stars with these measurements. Comparison with cosmological zoom-in simulations and these observations will greatly advance our understanding of the chemo-dynamical properties of dwarf galaxies. This study aims to understand the relationship between star formation and chemical evolution in satellite galaxies. With our high-resolution cosmological zoomin simulation of a MW-like galaxy, we examine SFHs, MDFs, and \u03b1-element abundances in satellites with M\u2217 \u223c105\u2013107 M\u2299, corresponding to the mass ranges of satellite dSphs of the MW. We show how SFHs are reflected in MDFs and \u03b1-element abundances using our simulation. We then evaluate the capability of upcoming surveys to reconstruct the SFHs from the chemical abundances of dwarf galaxies. This paper is organized as follows. Section 2 describes our code, the adopted initial conditions, and the procedures used for carrying out mock observations. In Section 3, we describe the chemo-dynamical properties of our simulated satellites. Section 4 discusses how SFHs are reflected in chemical abundances, and how these can be observed in future surveys. Our conclusions are presented in Section 5. 2. METHODS 2.1. Code We have computed the evolution of satellite galaxies in a cosmological zoom-in simulation of a MW-like Simulated Dwarf Satellites of the Milky Way 3 galaxy performed by Hirai et al. (2022). In this simulation, we adopted the N-body/density-independent smoothed particle hydrodynamics code asura (Saitoh et al. 2008, 2009; Saitoh & Makino 2013, 2016). For cooling and heating calculations, we adopted cloudy ver. 13.05 (Ferland et al. 2013). Gas particles probabilistically form stars if they are in a region with a number density of hydrogen atoms higher than 100 cm\u22123, the temperature is lower than 1,000 K, and there are converging flows (\u2207\u00b7 v < 0, e.g., Hirai et al. 2021). Each star particle is treated as a simple stellar population (SSP) with the initial mass function (IMF) of Chabrier (2003) from 0.1 M\u2299to 100 M\u2299. Star particles with ages less than 10 Myr heat the surrounding gas to 104 K (Fujii et al. 2021). We implemented momentum-based supernova feedback following Hopkins et al. (2018a). Metal diffusion was incorporated following Hirai & Saitoh (2017). The cosmic ultra-violet (UV) heating was implemented following Haardt & Madau (2012). The reionization is assumed to occurat a redshift (z) of 8.5. We also assumed the self-shielding model of Rahmati et al. (2013). We adopted the nucleosynthetic yields compiled in the Chemical Evolution Library (celib, Saitoh 2017). CCSNe and SNe Ia are the dominant contributors to the evolution of the [\u03b1/Fe] ratios. For CCSNe, we use the yields of Nomoto et al. (2013) with 13 M\u2299to 40 M\u2299. Given the mass of the star particle, we integrated the IMF from the maximum stellar mass of the IMF to the lower stellar mass until the cumulative number of stars in the integration range became unity. This approach enabled the tracking of the contribution from CCSNe with different progenitor masses in sufficiently high-resolution simulations. When the stellar particle mass (m\u2217) was 4.5 \u00d7 103 M\u2299, the IMF for CCSNe (13\u2013 40 M\u2299) was divided into 100 bins. For SNe Ia, we assumed a delay-time distribution with a power-law index of \u22121, and a minimum delay time of 40 Myr, following Maoz et al. (2012). We also included the contribution of asymptotic giant branch (AGB) stars for stars with 1 to 8 M\u2299(Karakas 2010; Doherty et al. 2014). We adopted the solar abundance of Asplund et al. (2009). 2.2. Initial Conditions A MW-like halo was selected from the cosmological simulation with a box size of (36 h\u22121 Mpc)3. We adopted cosmological parameters of \u2126m = 0.308, \u2126\u039b = 0.692, \u2126b = 0.0484, and H0 = 67.8 km s\u22121 Mpc\u22121 (Planck Collaboration et al. 2016). An initial condition for the zoom-in simulation was generated by music (Hahn & Abel 2011). We used the Amiga Halo Finder (ahf, Gill et al. 2004; Knollmann & Knebe 2009) to find Table 1. List of Simulated Satellite Galaxies at z = 0. Halo ID Mhalo M\u2217 \u27e8[Fe/H]\u27e9 \u03c3[Fe/H] d (M\u2299) (M\u2299) (dex) (kpc) 9 7.5 \u00d7 109 7.5 \u00d7 106 \u22121.95 0.23 204.2 12 4.7 \u00d7 109 2.1 \u00d7 107 \u22121.08 0.58 148.8 36 2.2 \u00d7 109 1.1 \u00d7 107 \u22121.43 0.37 54.5 38 2.5 \u00d7 109 1.3 \u00d7 105 \u22121.52 0.52 198.7 40 2.3 \u00d7 109 3.9 \u00d7 106 \u22121.52 0.46 57.9 150 5.9 \u00d7 108 2.4 \u00d7 105 \u22122.53 0.24 190.7 151 6.0 \u00d7 108 7.7 \u00d7 104 \u22122.89 0.43 167.2 167 5.2 \u00d7 108 3.1 \u00d7 104 \u22124.34 0.14 206.6 199 4.2 \u00d7 108 2.8 \u00d7 104 \u22123.42 0.28 169.2 Note\u2014From left to right, the columns are the Halo ID, the total halo mass within the virial radius (Mhalo), the total stellar mass (M\u2217), the mean [Fe/H] (\u27e8[Fe/H]\u27e9), the dispersion of [Fe/H] (\u03c3[Fe/H]), and the distance from the center of the central galaxy (d). M\u2217, \u27e8[Fe/H]\u27e9, and \u03c3[Fe/H] are computed within the half-mass radius. the target halo. In this simulation, the initial masses of each particle in the finest region were 7.2 \u00d7 104 M\u2299for dark matter, 1.3 \u00d7 104 M\u2299for gas, and 4.5 \u00d7 103 M\u2299for stars. We set the gravitational softening length (\u03f5g) to 85 pc for dark matter and 82 pc for gas and stars. We performed the simulation from z = 100 to 0. In this simulation, we picked out satellites orbiting the central galaxy. We only considered those with a minimum of 104 dark matter and 10 star particles, and made sure that they were not false substructures introduced by the contamination from low-resolution particles. Table 1 lists the simulated satellite galaxies selected for this study. 2.3. Mock Observations We performed mock observations for Subaru PFS (see Section 4.2)2. For the mock observation, we computed the magnitudes of simulated stars. First, SSP particles were divided into individual stars. In this model, stars from 0.1 M\u2299to 100 M\u2299were probabilistically generated from SSP particles, following a Chabrier (2003) IMF. Stars were generated until the total generated stellar mass exceeded the particle\u2019s mass. Then, the magnitudes of each star were computed using the isochrone 2 Sanderson et al. (2020) also discussed in detail mock observations of galaxy simulations. 4 Hirai et al. table obtained from cmd 3.73 (Girardi et al. 2000, and updates thereof). We generated isochrones with ages from 4 Gyr to 13.8 Gyr and [M/H]4 from \u22122.0 to 0.0 based on the PARSEC-COLIBRI stellar-evolutionary tracks (Bressan et al. 2012; Chen et al. 2014, 2015; Tang et al. 2014; Marigo et al. 2017; Pastorelli et al. 2019, 2020). With this tool, we computed apparent V -band magnitudes for stars in Halos 12 and 40. We assume Halos 12 and 40 are located at 147 kpc and 86 kpc from an observer to compare with the Fornax and Sculptor dSphs, respectively (McConnachie 2012). We then applied the Subaru PFS spectral synthesis pipeline (roughly based on Kirby et al. 2010; Escala et al. 2019) to compute observed uncertainties. The pipeline adopts synthetic spectra of K-giants and G-dwarfs for \u22124.0 \u2264[Fe/H] \u2264\u22120.5. We calculated wavelengthdependent continuum signal-to-noise ratios with the Subaru PFS Exposure Time Calculator5 using the simulated stars\u2019 V -band magnitudes, assuming a three-hour exposure in the Subaru PFS median-resolution mode for K giants. Then, we computed uncertainties on [Fe/H] and [\u03b1/Fe] by resampling the synthetic spectra hundreds of times from Gaussian-distributed per-pixel noise inversely proportional to the estimated signal-to-noise ratios. The simulated chemical abundances of stars are varied within those estimated uncertainties. 3. RESULTS 3.1. Structures and Star Formation Histories This paper mainly discusses the chemo-dynamical evolution of Halos 12, 40, and 150, listed in Table 1. The [\u03b1/Fe] as a function of [Fe/H] for Halos 9 and 36 are shown in the Appendix. We select three these simulated dwarf galaxies based on their stellar mass (Halo 12: 2.1 \u00d7 107M\u2299, Halo 40: 3.9 \u00d7 106M\u2299, and Halo 150: 2.4 \u00d7 105M\u2299). These values are similar to those of the Fornax (2.0 \u00d7 107M\u2299), Sculptor (2.3 \u00d7 106M\u2299), and Draco (2.9 \u00d7 105M\u2299) dSphs (McConnachie 2012). Also, Halos 12, 40, and 150 currently contain no gas. Figure 1 shows the stellar mass distribution of Halos 12, 40, and 150 at z = 0. The half-mass (light) radii of these galaxies are 1,334 pc (Halo 12), 874 pc (Halo 40), and 1,346 pc (Halo 150), respectively. The somewhat larger radii than the observed ones (Fornax: 710 pc, Sculptor: 283 pc, Draco: 221 pc, McConnachie 2012) are 3 http://stev.oapd.inaf.it/cgi-bin/cmd 4 [M/H] = log(Z/X) \u2212log(Z/X)\u2299, where X and Z are the mass fractions of hydrogen and metals, respectively. 5 https://github.com/Subaru-PFS/spt ExposureTimeCalculator due to the spatial resolution of this simulation (\u03f5g = 85 pc). The simulated satellite dwarf galaxies exhibit various SFHs. Figure 2 shows the cumulative SFHs of all satellites listed in Table 1. The SFHs of satellite galaxies are affected by SN feedback, cosmic reionization, and interactions with the host galaxy. This figure shows that more massive satellites tend to have extended SFHs, while less massive halos quench star formation earlier. Star formation in halos with < 109M\u2299(150, 151, 167, and 199) is quenched at < 2 Gyr from the beginning of the simulation by cosmic reionization and SN feedback, while halos with \u2265109M\u2299form stars after the reionization epoch. Gas accreted before reionization in halos with \u2265109M\u2299self-shield the UV background, resulting in them surviving the reionization (e.g., O\u02dc norbe et al. 2015; Wheeler et al. 2019). Hereafter, we focus on three satellites: Halos 12, 40, and 150. The mass and the cosmic infall time also affect the SFHs. Figure 3 shows the orbits (top panels), mass evolution (middle panels), and SFHs (bottom panels) of Halos (a) 12, (b) 40, and (c) 150. Halo 12 has the most recent infall time. The first pericentric passage (5 kpc) of this galaxy is 0.7 Gyr prior to the end of the simulation (Figure 3 (a), top panel). Prior to pericentric passage, this galaxy experienced two star formation events separated by 2.9 Gyr (Figure 3 (a), bottom panel). The first period of star formation starts at 0.1 Gyr and ends at 3.3 Gyr from the beginning of the simulation. During this period, stars are formed along with the accretion of material (Figure 3 (a), middle panel). After SNe expel the gas away from the halo, the infall of the gas forms new stars. This interplay episodically forms stars for 3.2 Gyr. The second star formation event begins when the accretion of a halo brings additional material to the halo at 6.2 Gyr. As with the first period of star formation, it is regulated by SN feedback. The star formation is quenched when feedback from CCSNe from the recent star formation (t \u227210 Myr ago) and SNe Ia from previous star formation (t \u223c1 Gyr ago) expel the gas from the galaxy at 9.5 Gyr. Halo 40 has a shorter total duration of star formation, mainly due to the earlier infall time than that of Halo 12. Halo 40 crosses the main halo\u2019s virial radius (Rvir) at 7.4 Gyr, while Halo 12 experiences its closest pericenter passage at 12.6 Gyr. Due to the early infall, repeated gas removal by ram pressure stripping prevents additional star formation in the later phase. The evolution of gas mass after the first infall is due to our analysis method. The increase in the tidal radius of the halo around the apocenter accretes more diffuse gas around the galaxy, Simulated Dwarf Satellites of the Milky Way 5 \u22124 \u22122 0 2 4 X (kpc) \u22124 \u22122 0 2 4 Y (kpc) (a) \u22125.0 \u22124.5 \u22124.0 \u22123.5 \u22123.0 \u22122.5 Log stellar mass fraction \u22124 \u22122 0 2 4 X (kpc) \u22124 \u22122 0 2 4 Y (kpc) (b) \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 Log stellar mass fraction \u22124 \u22122 0 2 4 X (kpc) \u22124 \u22122 0 2 4 Y (kpc) (c) \u22125.0 \u22124.5 \u22124.0 \u22123.5 \u22123.0 \u22122.5 Log stellar mass fraction Figure 1. Stellar distribution of simulated satellite dwarf galaxies for (a) Halo 12, (b) Halo 40, and (c) Halo 150. The color scale depicts each grid\u2019s log scale stellar-mass fraction. Most stars are spherically distributed at the center of their dark matter halo. resulting in the increase of the detected gas mass of this 100 101 log(Time (Gyr)) 0.0 0.2 0.4 0.6 0.8 1.0 Cumulative star formation history Halo 9 Halo 12 Halo 36 Halo 38 Halo 40 Halo 150 Halo 151 Halo 167 Halo 199 Figure 2. Cumulative SFHs of simulated dwarf satellites, as listed in Table 1. Less massive halos (e.g., Halos 151, 167, and 199) tend to quench star formation earlier than more massive halos (e.g., Halos 9, 12, and 36). halo. Although gas mass evolution is shown here, these gas particles are not eligible to form stars. Halo 40 experienced star formation in the first 2.8 Gyr. As shown in the bottom panel of Figure 3 (b), there are five peaks of star formation, separated from 0.40 to 0.97 Gyr. The SFH in this halo is also mainly regulated by SN feedback. As shown in the bottom panel of Figure 3 (b), stars are formed during cosmic reionization. After the star formation is quenched at 0.83 Gyr, an additional gas supply resumes star formation at 1.79 Gyr. Eventually, star formation is halted at 2.76 Gyr. This quenching is mainly caused by the heating by CCSNe from the recent star formation and SNe Ia from the previous star formation, due to their delay times. Since Halo 40 is located at a distance five times larger than the virial radius of the main halo at 2.76 Gyr, ram pressure stripping is unlikely to be the main cause responsible for the suppression of star formation. Halo 150 has the shortest duration of star formation among the halos shown in Figure 3. Figure 3 (c) shows the cosmic time evolution of Halo 150. The top panel shows that this halo experienced at least two pericenter passages. Note that we cannot follow the mass evolution before 4.84 Gyr, because the progenitor halos are undetected by the halo finder. As shown in the bottom panel of Figure 3 (c), the first episode of star formation lasts 0.47 Gyr, and is quenched by cosmic reionization. In this episode, 80% of its stars are formed. The second star formation event occurs at 1.66 Gyr, possibly because of the gas infall, but it is quenched quickly. 6 Hirai et al. 0 1000 Distance (kpc) 106 109 Mass (M ) 0 2 4 6 8 10 12 14 Time (Gyr) 10 3 10 2 SFR (M  yr 1) (a) 0 500 1000 Distance (kpc) 106 109 Mass (M ) 0 2 4 6 8 10 12 14 Time (Gyr) 10 3 10 2 SFR (M  yr 1) (b) 0 200 Distance (kpc) 105 107 109 Mass (M ) 0 2 4 6 8 10 12 14 Time (Gyr) 10 3 SFR (M  yr 1) (c) Figure 3. Cosmic time evolution of (a) Halo 12, (b) Halo 40, and (c) Halo 150. Top sub-panels: The orbital distance (blue) and the time evolution of the virial radius of the main halo (orange). Middle sub-panels: The dark matter (bluesolid) and gas (orange-dashed) mass evolution. Bottom subpanels: star formation histories. The grey line represents the epoch of reionization (z = 8.5). The light-grey shaded region in panel (c) means the halo finder cannot follow the mass evolution. 3.2. Chemical Abundances The MDFs of stellar systems reflect their histories of star formation, gas infall, and gas outflow; Figure 4 shows MDFs of Halos 12, 40, and 150. We also plot the observed MDFs of the Fornax, Sculptor, and Draco dSphs (Kirby et al. 2010). It should be noted that the purpose of our study is not to reproduce the MDFs of the observed dSphs. Rather, we compare simulated and observed MDFs in Section 4.1. The MDF of Halo 12 exhibits a bimodal distribution, reflecting two major star formation events (the bottom panel of Figure 3 (a)). All stars with [Fe/H] < \u22121.5 are formed within 3.3 Gyr from the beginning of the simulation. These stars are mainly located in the outskirts of the galaxy. For stars with [Fe/H] < \u22121.5, 28.5% of them are within rh, while 71.5% of stars with [Fe/H] \u2265\u22121.5 are within rh. As shown in the green-dashed line in Figure 4 (a), the fraction of stars with [Fe/H] < \u22121.5 in the MDF is significantly decreased for stars within rh. Stars around [Fe/H] = \u22121.2 and [Fe/H] = \u22120.8 are associated with star formation events around 8.0 Gyr and 9.5 Gyr, respectively. As shown in the middle panel of Figure 3 (a), these stars are formed from gas infall. Figure 4 (b) shows the MDF of Halo 40. The MDF is broadly distributed over \u22123.0 \u2272[Fe/H] \u2272\u22121.0. Stars around [Fe/H] = \u22122.3, \u22121.8, and \u22121.3 reflect star formation at different cosmic times. For [Fe/H] < \u22122.5, all stars formed before 1.0 Gyr from the beginning of the simulation. For stars with \u22122.5 < [Fe/H] < \u22122.0, half of them are formed at t < 1.0 Gyr, while others are formed at 1.7 < t/(Gyr) < 2.3, simultaneously with stars with \u22122.0 < [Fe/H] < \u22121.5. Stars with [Fe/H] > \u22121.5 have younger ages. All of these stars are formed after 2.2 Gyr. Although there is an overlap in the ages of each peak, the peaks in the MDFs indicate star formation at different cosmic times. In Figure 4 (b), we also plot the MDF for stars within rh. Unlike for Halo 12, the MDFs are not largely affected by the spatial distribution of stars. Figure 4 (c) shows the MDF for Halo 150. As shown in Figure 3 (c), Halo 150 exhibits two star formation events. The second peak of star formation produces stars with \u22122.3 < [Fe/H] < \u22122.1, while the first star formation event mainly forms stars with [Fe/H] < \u22124.0. The number fraction of these ultra metal-poor (UMP) stars is 75.6% for all UMP stars and 64.9% for UMP stars within rh. These stars largely affect the median metallicity of this galaxy. The median metallicity is [Fe/H] = \u22124.36 for all stars, but [Fe/H] = \u22122.16 for stars with [Fe/H] > \u22124.0. Stars with different ages clearly differ in the [\u03b1/Fe] vs. [Fe/H] space. Figure 5 (a) shows [\u03b1/Fe], as a function of [Fe/H], in Halo 12. This galaxy has two major Simulated Dwarf Satellites of the Milky Way 7 \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 df/d[Fe/H] (a) Halo 12 Halo 12 (within rh) Fornax \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] 0.00 0.05 0.10 0.15 0.20 0.25 df/d[Fe/H] (b) Halo 40 Halo 40 (within rh) Sculptor \u22126 \u22125 \u22124 \u22123 \u22122 \u22121 [Fe/H] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 df/d[Fe/H] (c) Halo 150 Halo 150   (within rh) Draco Figure 4. Simulated (blue-solid line) and observed (orangedashed line) MDFs for (a) Halo 12 and Fornax, (b) Halo 40 and Sculptor, and (c) Halo 150 and Draco. The green-dashed line represents the MDFs for stars within rh. The simulated data do not include simulated observational errors. Observed data are taken from Kirby et al. (2010). star formation events (Figure 3 (a)). The first event (13.7 Gyr to 10.5 Gyr ago) forms the decreasing trend of [\u03b1/Fe] from [Fe/H] = \u22122.5 to [Fe/H] = \u22121.0. Also, there is roughly a \u223c1 dex scatter in the [\u03b1/Fe] ratios. The episodic star formation creates these features during the first major star formation event. The first star formation episode (\u226513 Gyr ago) forms the high-\u03b1 ([\u03b1/Fe] > +0.3) component. The interstellar medium (ISM)\u2019s inhomogeneity results in a widely distributed metallicity (\u22123.0 < [Fe/H] < \u22121.5). The low-\u03b1 (\u22120.3 < [\u03b1/Fe] < \u22120.1) and very metal-poor (\u22122.5 < [Fe/H] < \u22122.2) component come from another dwarf galaxy accreted to Halo 12. The subsequent star formation episodes (12.0 Gyr to 10.5 Gyr ago) produce the decreasing trend of [\u03b1/Fe] ratios due to the substantial contribution from SNe Ia. In contrast, the second star formation event (7.6 Gyr to 4.3 Gyr ago) produces an increasing trend of the [\u03b1/Fe] ratios for [Fe/H] > \u22121.5. This trend suggests that stars are preferentially formed from the ejecta of CCSNe. During the second major star formation event, stars are mainly produced at the galaxy\u2019s center. Young stars give rise to CCSNe mainly at the center, while SNe Ia occur in the more extended region due to their delay times; SNe Ia occur in the more distant places relative to the star-forming region. This difference in the spatial distribution results in the formation of stars reflecting the yields of CCSNe. Since Si also exhibits a similar behavior, AGB stars are unlikely to contribute to forming this trend. Figure 5 (b) shows [\u03b1/Fe], as a function of [Fe/H], in Halo 40. From inspection, five peaks of star formation (Figure 3 (b)) produce groups of stars with different [Fe/H] and [\u03b1/Fe] ratios. The first peak of star formation (13.4 Gyr ago) produces stars with [Fe/H] < \u22122.3 and [\u03b1/Fe] > +0.3. Since it is the earliest phase of the star formation, CCSNe are the dominant contributor to the enrichment, resulting in a flat trend of [\u03b1/Fe] as a function of [Fe/H]. A few stars with [Fe/H] > \u22122.0 and [\u03b1/Fe] \u22480.2 are formed from the ejecta of Population III CCSNe. The second peak of star formation (13.0 Gyr ago) forms stars with \u22122.5 < [Fe/H] < \u22122.0 and +0.1 < [\u03b1/Fe] < +0.5. The contribution of SNe Ia from the stars produced in the first peak of star formation makes this second group of stars, with lower [\u03b1/Fe] and higher [Fe/H] than the first group. Subsequent star formation and the contributions of SNe Ia from the previous peaks of star formation produce groups of stars with lower [\u03b1/Fe] and higher [Fe/H]. The third peak of star formation (12.0 Gyr ago) creates groups of stars with \u22122.5 < [Fe/H] < \u22121.7 and \u22120.3 < [\u03b1/Fe] < +0.2. This group has the lowest [\u03b1/Fe] 8 Hirai et al. ratios because of the contribution of SNe Ia from the previous two star formation peaks. The fourth peak of star formation (11.6 Gyr ago) produces stars with the same [Fe/H] range but higher [\u03b1/Fe] ratios (0.0< [\u03b1/Fe] < +0.4). This group of stars reflects the ejecta from CCSNe formed in the third peak of star formation. The final star formation event (11.0 Gyr ago) forms stars with \u22121.5 < [Fe/H] < \u22121.0 and \u22120.2 < [\u03b1/Fe] < +0.2. Because of its short duration (\u223c100 Myr), stars are mainly formed from the ejecta of CCSNe. Figure 5 (c) shows [\u03b1/Fe] as a function of [Fe/H] in Halo 150. Although stars are too few to discuss the trend of the [\u03b1/Fe] ratios, stars formed at different times exhibit distinct differences in [\u03b1/Fe] ratios. Stars formed in \u226513.4 Gyr ago show [\u03b1/Fe] > +0.2, reflecting the yields of CCSNe. Different [\u03b1/Fe] ratios originate from CCSNe with different progenitor masses. A clear separation of star formation events (1.24 Gyr, Figure 3 (c)) yields stars formed in the second star formation peak with lower [\u03b1/Fe] ratios owing to the contribution of SNe Ia. The dispersion of the [\u03b1/Fe] ratios reflects the degree of the ISM\u2019s inhomogeneity. We quantified the scatter for [\u03b1/Fe] in \u22123 < [Fe/H] < \u22120.5 following Escala et al. (2018). These authors defined the intrinsic scatter as the standard deviation of the distance distribution between stars\u2019 [\u03b1/Fe] ratios and the cubic spline fitting curve for the data. For Halos 12 and 40, the intrinsic scatter of [\u03b1/Fe] is 0.18 dex and 0.16 dex, respectively. These are similar to the estimated intrinsic scatter (Escala et al. 2018) of the Fornax (0.14 dex) and Sculptor dSphs (0.078 dex), meaning that the simulated and observed satellites have ISM inhomogeneity that gives rise to scatter \u22720.2 dex for the [\u03b1/Fe] ratios. The radial metallicity distribution reflects spatial variations in star formation. Star formation in the inner region of Halos 12 and 40 lasts longer than that in the outer region. Figures 6 (a) and (b) show radial [Fe/H] distributions in Halos 12 and 40, respectively. Both galaxies have a negative slope of [Fe/H], as a function of the distance from the center, reflecting the difference in the spatial distribution of the stars with different ages. The youngest stars in these galaxies are located within 3 kpc, while stars with ages of > 13 Gyr have a more extended spatial distribution to 5 kpc. The radial [\u03b1/Fe] distribution exhibits positive slopes (Figures 6 (c) and (d)). Because newer stars located in the center of the galaxies are more affected by SNe Ia, the average [\u03b1/Fe] ratio near the galactic center is lower than in the outskirts. These radial [Fe/H] and [\u03b1/Fe] gradients are caused by old and metal-poor populations in the outskirts. This result highlights the importance \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] \u22120.50 \u22120.25 0.00 0.25 0.50 0.75 1.00 [\u03b1/Fe] (a) 6 8 10 12 Age (Gyr) \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] \u22120.50 \u22120.25 0.00 0.25 0.50 0.75 1.00 [\u03b1/Fe] (b) 11.0 11.5 12.0 12.5 13.0 13.5 Age (Gyr) \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] \u22120.50 \u22120.25 0.00 0.25 0.50 0.75 1.00 [\u03b1/Fe] (c) 12.05 12.06 12.07 12.08 12.09 12.10 Age (Gyr) Figure 5. The \u03b1-element distributions for (a) Halo 12, (b) Halo 40 , and (c) Halo 150. The color bars indicate the ages of the stars. The simulated data do not include simulated observational errors. of measuring the chemical abundances of stars in the outer regions of dwarf satellites. The kinematics of stars also differ among stars with different metallicities. Figures 7 (a) and (b) show the line-of-sight velocities (vlos) as a function of [Fe/H]. We computed vlos assuming that Halos 12 and 40 are located in the equatorial coordinates of Fornax and Sculptor (Hayashi et al. 2020), respectively, i.e., we observed Halos 12 and 40 respectively located in the positions of Fornax and Sculptor dSphs from the position of the Sun in the Milky Way. The dispersion of vlos for [Fe/H] \u2264\u22121.5 is 19.3 km s\u22121 in Halo 12 and 19.2 km s\u22121 in Halo 40. On the other hand, stars with [Fe/H] > \u22121.5 have smaller dispersion: 15.0 km s\u22121 (Halo 12) and 16.8 km s\u22121 (Halo 40). These results confirm the existence of kinematical distinct populations in satellites (e.g., Tolstoy et al. 2004; Battaglia et al. 2006). Simulated Dwarf Satellites of the Milky Way 9 0 1 2 3 4 5 Distance from the center (kpc) 3.0 2.5 2.0 1.5 1.0 0.5 [Fe/H] (a) ( 0.22 \u00b1 0.01) dex per kpc 5 6 7 8 9 10 11 12 13 Age (Gyr) 0 1 2 3 4 5 Distance from the center (kpc) 3.0 2.5 2.0 1.5 1.0 0.5 [Fe/H] (b) ( 0.13 \u00b1 0.01) dex per kpc 11.0 11.5 12.0 12.5 13.0 13.5 Age (Gyr) 0 1 2 3 4 5 Distance from the center (kpc) 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 [ /Fe] (c) (+0.05 \u00b1 0.002) dex per kpc 5 6 7 8 9 10 11 12 13 Age (Gyr) 0 1 2 3 4 5 Distance from the center (kpc) 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 [ /Fe] (d) (+0.08 \u00b1 0.01) dex per kpc 5 6 7 8 9 10 11 12 13 Age (Gyr) Figure 6. Radial [Fe/H] distributions for (a) Halo 12, (b) Halo 40, and [\u03b1/Fe] distributions for (c) Halo 12, and (d) Halo 40, respectively. The color bars indicate the ages of the stars. The simulated data do not include simulated observational errors. The red line is the least squares linear fit for the data. The slope is shown in each panel. 4. DISCUSSION 4.1. Chemo-dynamical Evolution of Satellites Here, we discuss the chemo-dynamical evolution of the MW\u2019s satellites by comparing simulations and observations. The relationship between orbits and SFHs has been argued to explain the variety of observed SFHs seen in MW\u2019s satellites. Miyoshi & Chiba (2020) computed the orbital motions of MW\u2019s satellites, including Fornax, Leo I, Sculptor, and Draco, with a time-varying gravitational potential based on the Gaia Data Release 2 (Gaia Collaboration et al. 2018) proper motions, and compared them with SFHs. They found that the infall times of classical dSphs coincide well with the peak of the star-formation regions (SFRs), while UFDs had already been quenched before the infall times. Simulated satellites have some similarities to galaxies analyzed by Miyoshi & Chiba (2020). Halo 12 is similar to the Fornax dSph in terms of its stellar mass and SFH. Both galaxies have intermediate age (4\u20138 Gyr) and old (> 10 Gyr) stellar populations. The orbit of Halo 12 is similar to that of Leo I. Both Halo 12 and Leo I experienced one pericenter passage throughout their orbits. Stellar mass, orbits, and SFHs are similar between Halo 40 and the Sculptor dSph. These galaxies formed most stars prior to their infall. Halo 150 is similar to the Draco dSph regarding stellar mass, orbits, and SFHs. These galaxies also comprise old (> 10 Gyr) stellar populations. These results suggest that star formation in intermediate-age and old stars in these galaxies was regulated by SN feedback and gas inflow, as we have argued in Section 3.1. The major difference between our simulation and the MW\u2019s satellites is the star formation after infall. Our simulation does not exhibit enhancement of the SFR at the time of the infall, which has been observed by 10 Hirai et al. 3.0 2.5 2.0 1.5 1.0 0.5 [Fe/H] 0 20 40 60 80 100 120 vlos (km s 1) (a) 3.0 2.5 2.0 1.5 1.0 0.5 [Fe/H] 50 75 100 125 150 175 vlos (km s 1) (b) Figure 7. Line-of-sight velocities (vlos) as a function of [Fe/H] in (a) Halo 12 and (b) Halo 40. The simulated data do not include simulated observational errors. The orangedashed line shows the standard deviation of vlos as a function of [Fe/H]. Miyoshi & Chiba (2020). Di Cintio et al. (2021) showed that galaxies should satisfy two conditions to enhance the star formation after infall: (1) galaxies must have cold gas with at least 10\u22122 times the virial mass of the halo at the time of the infall and (2) the pericentric distance should be larger than 10 kpc. None of the galaxies analyzed in this study satisfy these conditions. The strength and treatment of SN feedback highly affect the SFHs and gas outflow of simulated dwarf galaxies. Since galaxy formation simulations cannot resolve the evolution of SN remnants, we need to rely on subgrid feedback models (e.g., Naab & Ostriker 2017; Hopkins et al. 2018a). Revaz & Jablonka (2012) performed isolated dwarf galaxy simulations with different strengths of SN feedback. Their simulations showed that the star formation lasted < 1 Gyr in their strongest feedback case, while stars were continuously formed over 14 Gyr if they adopted a level of feedback 100 times less than the strongest one (also see Hazenfratz et al. 2024). Xu et al. (2022) suggested that the mass-loading factor (the ratio of outflow rate and star formation rate) in dwarf galaxies (M\u2217\u223c104\u2013107M\u2299) observed in extremely metal-poor representatives explored by the Subaru survey project (e.g., Kojima et al. 2020; Matsumoto et al. 2022; Isobe et al. 2023; Nishigaki et al. 2023; Xu et al. 2024) were \u223c10 to 100 times lower than those predicted in galaxy formation simulations. These results highlight the importance of studying the effects of feedback on the SFHs of dwarf galaxies. MDFs reflect the SFHs and gas infall/outflow of dwarf galaxies. Kirby et al. (2011b) showed that Fornax dSph has a narrow MDF with \u03c3 = 0.36 dex. The Leo I dSph also exhibits a similar MDF. Their chemical evolution model suggested that these galaxies experienced gas infall to shape the narrow MDF. Halo 12 also exhibits a narrow MDF (\u03c3 = 0.20 dex) for stars with [Fe/H] > \u22121.5. As described in Section 3, these stars are formed by gas infall. These results suggest that gas infall plays an important role in the chemical evolution of the Fornax and Leo I dSphs. The Sculptor dSph has a broader MDF (\u03c3 = 0.46 dex) than those of the Fornax and Leo I dSphs (Kirby et al. 2013). Kirby et al. (2011b) found that none of their chemical evolution models reproduce Sculptor\u2019s MDF. This problem is resolved if they alter the SFH of the chemical evolution model to a more appropriate choice of parameters for SNe Ia and the SFH (Kirby et al. 2011a; Homma et al. 2015). Homma et al. (2015) interpreted Sculptor\u2019s SFH derived by de Boer et al. (2012a) with a chemical evolution model similar to that of Kirby et al. (2011b). They found that dSphs with a larger fraction of stars formed in the early phase have a more elongated low-metallicity tail of the MDF. Halo 40 in our simulation also exhibits a broad MDF (\u03c3 = 0.46 dex) similar to Sculptor\u2019s MDF. This broad MDF is formed by episodic star formation (Figure 3 (b)), rather than the continuous SFH assumed in the one-zone chemical evolution models (Kirby et al. 2011a; Homma et al. 2015). From inspection of Figure 4 (b), there are at least three distinct peaks in Halo 40\u2019s MDF formed by episodic star formation. If this is the case, upcoming spectroscopic surveys of dSphs could confirm whether or not the Sculptor dSph has an episodic SFH (see Section 4.2). 4.2. Prospects for Future Surveys Identifying whether the MW\u2019s satellites have episodic star formation is critical to understanding the effects of SN feedback on their chemo-dynamical evolution and the nature of dark matter (e.g., Aparicio et al. 2001; Bettinelli et al. 2019; Rusakov et al. 2021). Pontzen & Governato (2012) showed that large-scale bulk motion Simulated Dwarf Satellites of the Milky Way 11 of gas caused by episodic star formation transforms the cusped density profile of dark matter to a cored one (also see Mashchenko et al. 2008; Wheeler et al. 2019). The dependence of SFHs on dark matter profiles in observed satellites is not well understood (e.g., Hayashi et al. 2020, 2023). We need additional indicators to identify episodic star formation. As we have found in Figure 5, the episodic star formation creates groups of stars with similar [\u03b1/Fe] and [Fe/H]. We need to search for this feature with observations. Upcoming wide-field spectroscopic surveys will be able to measure chemical abundances for a sufficiently large number of stars to detect signatures of episodic SFH from chemical abundances (e.g., Takada et al. 2014; Cooper et al. 2023). For example, Subaru PFS will measure Fe and \u03b1-element abundances for 14,000 and 6,900 stars in Fornax and Sculptor, respectively. In this subsection, we discuss how the simulated [\u03b1/Fe] vs. [Fe/H] distribution (Figure 5) can be observed by Subaru PFS. Figure 8 shows Subaru PFS mock observations of [\u03b1/Fe] vs. [Fe/H] for Halos 12 and 40. Procedures for the mock observations are described in Section 2.3. Typical observational uncertainties added to the simulated data are \u03c3 \u22480.13 dex and 0.14 dex for the [\u03b1/Fe] and [Fe/H] ratios, respectively. Compared to Figure 5, the scatter in the [\u03b1/Fe] ratios have been increased. Nevertheless, we can still identify groups of stars having similar [\u03b1/Fe] and [Fe/H] associated with episodic star formation. The top panel of Figure 8 compares mock observed abundances of Halo 12 and the Fornax dSph. With Keck/DEIMOS, Kirby et al. (2011a) found scatter in [\u03b1/Fe] ratios and a lack of correlation with [Fe/H] in Fornax. Their results suggested that such scatter could arise from bursty star formation or inhomogeneity of the ISM. Mock observed [\u03b1/Fe] ratios in Halo 12 also exhibit scatter for stars with [Fe/H] > \u22121.5. Due to the observed uncertainties, detailed structures of [\u03b1/Fe] ratios seen in Figure 5 (a) cannot be observed, and these structures are observed as scatter. As we have argued in Section 3.2, the scatter of [\u03b1/Fe] ratios likely come from the enhanced contribution of CCSNe, due to bursty star formation and inhomogeneous chemical abundances in the ISM. This result is consistent with the suggestion by Kirby et al. (2011a). Stars with [Fe/H] < \u22121.5 in Figure 8 (top) highlight the importance of observing the Fornax dSph with a wide-field multiplexed spectrograph. In Figure 4 (a), we have shown that most stars with [Fe/H] < \u22121.5 are located outside of rh. Even after applying observed uncertainties, we can still see the decreasing trend of [\u03b1/Fe] as a function of [Fe/H] and scatter associated with the Figure 8. Subaru PFS mock observations (black dots) of [\u03b1/Fe] vs. [Fe/H] for Halos 12 (top panel) and 40 (bottom panel). Red symbols are the abundances for Fornax (top panel) and Sculptor (bottom panel) observed with Keck/DEIMOS (Kirby et al. 2011a). peaks of episodic star formation. Since the current sample (Kirby et al. 2011b) is limited to the center of the Fornax dSph (\u2272400 pc), we cannot constrain the chemical evolution in the outskirts of this galaxy. We will be able to investigate the most metal-poor tail of the MDF and [\u03b1/Fe] ratios by obtaining spectroscopy out to the tidal radius (2,078 pc; Irwin & Hatzidimitriou 1995) of the Fornax dSph. There are limitations on the ability of mediumresolution spectroscopy to identify dwarf galaxies accreted to the Fornax dSph with [\u03b1/Fe] ratios. In Figure 5, we find a low-\u03b1 (\u22120.3 < [\u03b1/Fe] < \u22120.1) and very metal-poor (\u22122.5 < [Fe/H] < \u22122.2) component, which is from an accreted dwarf galaxy. However, the distinction of this component is unclear, due to the observed uncertainties in Figure 8 (top). This result suggests that measuring velocity distribution (Figure 7) and high-resolution spectroscopy for chemical abundances of stars on the outskirts is necessary to distinguish accreted components. For example, most stars with [Fe/H] 12 Hirai et al. \u2264\u22122.5 in Halo 12 come from accreted dwarf galaxies. Their line-of-sight velocity dispersion is 22.3 km s\u22121, while that of stars with [Fe/H] > \u22122.5 shows 16.7 km s\u22121 (Figure 7). These difference in velocity dispersion could be measured in future surveys. The bottom panel of Figure 8 compares mock observed [\u03b1/Fe], as a function of [Fe/H], in Halo 40 and the Sculptor dSph. In the mock observation, the groups of stars with similar [\u03b1/Fe] and [Fe/H] formed in episodic star formation. For [Fe/H] < \u22122.0, these groups are typically separated with 0.5 and 0.4 dex in [Fe/H] and [\u03b1/Fe], respectively. However, the number of stars (375) observed in Keck/DEIMOS (Kirby et al. 2011b) is insufficient to identify such groups of stars. With Subaru PFS, we expect to measure [\u03b1/Fe] and [Fe/H] for 6,900 stars in the Sculptor dSph. As shown in this mock observation, in the planned survey we will confirm whether there is episodic star formation occurring every few hundred Myr by identifying chemical clumps. In this subsection, we have shown that [\u03b1/Fe] vs. [Fe/H] measured by medium-resolution spectroscopy for \u22731,000 stars can confirm signatures of episodic star formation in the Fornax and Sculptor dSphs. Thanks to our high-resolution cosmological zoom-in simulation, we can discuss the detailed chemo-dynamical structures of satellite galaxies with \u2273106 M\u2299. However, due to the resolution limit, we cannot constrain the SFHs and chemical abundances of galaxies with \u2272105 M\u2299. The SFHs of poorly resolved galaxies tend to be more bursty, because there are too many synchronized SNe from a star particle (e.g., Hopkins et al. 2018b; GarrisonKimmel et al. 2019). Hopkins et al. (2018b) showed that simulated galaxies should have > 100 star particles to result in a convergence of SFHs. This result means that simulations of MW-like galaxies with a mass resolution of \u223c10 M\u2299is required to resolve SFHs of the smallest satellites (\u2272103 M\u2299). Such simulations could be achieved by resolving the computational scaling issue using deep learning (Hirashima et al. 2023). We expect that a comparison with upcoming wide-field spectroscopic surveys and high-resolution cosmological simulations will improve our capability to reconstruct the chemo-dynamical evolution of satellites from chemical abundances. 5. CONCLUSIONS In this study we performed a high-resolution cosmological zoom-in simulation of a MW-like galaxy. With this simulation, we find that the SFHs, MDFs, and [\u03b1/Fe] ratios of three simulated satellite galaxies are similar to the MW\u2019s satellites (Fornax, Sculptor, and Draco dSphs). We also performed a mock observation of medium-resolution spectra using the Subaru PFS spectral synthesis pipeline. In our simulation, we find that star formation in most simulated satellites is quenched before their infall to the host (Figure 3). Star formation episodes in simulated satellites are separated by a few hundred Myr. Such episodic star formation is regulated by SN feedback. For the Fornax-like galaxy (Halo 12), gas infall induces additional star formation at \u22486\u201310 Gyr from the beginning of the simulation. Simulated MDFs reflect SFHs and gas infall/outflow. The narrow MDF for [Fe/H] > \u22121.5 in Halo 12 is formed in the additional star formation due to gas infall (Figure 4 (a)). This feature is similar to the Fornax dSph. In contrast, the Sculptor-mass galaxy (Halo 40) exhibits a broad MDF (Figure 4 (b)). This MDF has at least three distinct peaks formed by episodic star formation. The [\u03b1/Fe] ratios, as a function of [Fe/H], reflect the ages of stars (Figure 5). The oldest stars have [\u03b1/Fe] \u2273+0.4. Subsequent enrichment by SNe Ia decreases the [\u03b1/Fe] ratios. Stars with similar ages formed in episodic star formation events comprise groups with similar [\u03b1/Fe] and [Fe/H]. The bursty star formation and inhomogeneity of the ISM form scattered [\u03b1/Fe] ratios at [Fe/H] > \u22121.5. Our mock observations find that the groups of stars with similar [\u03b1/Fe] and [Fe/H] formed by episodic star formation can be identified by upcoming multiplexed medium-resolution spectra surveys (Figure 8). We can test whether satellites have episodic star formation with [\u03b1/Fe] ratios measured with medium-resolution spectra for \u22731,000 stars. We also find that metal-poor stellar populations can be found in the outskirts of the galaxy. These results indicate that comparison with upcoming spectroscopic surveys and high-resolution cosmological simulations will greatly improve our understanding of the chemo-dynamical evolution of satellite galaxies. Simulated Dwarf Satellites of the Milky Way 13 This work was supported in part by JSPS KAKENHI Grant Numbers JP22KJ0157, JP21H04499, JP21K03614, JP22H01259, JP24K00669, JP20H01895, JP21K13909, JP23H04009, JP22K03688, JP20H05855, MEXT as \u201cProgram for Promoting Researches on the Supercomputer Fugaku\u201d (Structure and Evolution of the Universe Unraveled by Fusion of Simulation and AI; Grant Number JPMXP1020230406), JICFuS, grants PHY 14-30152; Physics Frontier Center/JINA Center for the Evolution of the Elements (JINA-CEE), and OISE-1927130: The International Research Network for Nuclear Astrophysics (IReNA), awarded by the US National Science Foundation. E.N.K. acknowledges support from NSF CAREER grant AST-2233781. Numerical computations and analysis were carried out on Cray XC50 and computers at the Center for Computational Astrophysics, the National Astronomical Observatory of Japan and the Yukawa Institute Computer Facility. This research made use of NASA\u2019s Astrophysics Data System. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Software: AHF (Gill et al. 2004; Knollmann & Knebe 2009), astropy (Astropy Collaboration et al. 2013, 2018), CELib (Saitoh 2017), Cloudy (Ferland et al. 2013), MUSIC (Hahn & Abel 2011) APPENDIX Figure 9 shows [\u03b1/Fe], as a function of [Fe/H], for Halos 9 and 36, which have sufficient data to plot. Halo 9 has two major star formation events in 2 Gyr. The first burst forms stars with [Fe/H] \u2272\u22122.0, and the second burst produces stars with [Fe/H] \u2273\u22122.0. As a result of Fe enrichment by SNe Ia, the [\u03b1/Fe] ratios decrease toward higher metallicity. The inhomogeneity of the spatial metallicity distribution of the ISM due to CCSNe produces scatter of the [\u03b1/Fe] ratios. On the other hand, Halo 36 has a more extended SFH (Figure 2). The first star formation event creates stars with constant [\u03b1/Fe] \u2248+0.3 due to the contribution from CCSNe. The two subsequent star formation events are influnced by SNe Ia. There is a decreasing trend of [\u03b1/Fe] ratios toward higher [Fe/H]. Similar to Halos 12 and 40, both galaxies have stars with different [\u03b1/Fe] and [Fe/H], depending on their ages. \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] \u22120.50 \u22120.25 0.00 0.25 0.50 0.75 1.00 [\u03b1/Fe] Halo 9 11.0 11.5 12.0 12.5 13.0 13.5 Age (Gyr) \u22123.0 \u22122.5 \u22122.0 \u22121.5 \u22121.0 \u22120.5 [Fe/H] \u22120.50 \u22120.25 0.00 0.25 0.50 0.75 1.00 [\u03b1/Fe] Halo 36 9 10 11 12 13 Age (Gyr) Figure 9. Same as Figure 5, but for Halos 9 (left) and 36 (right). The color bars indicate the ages of the stars. 14 Hirai et al.",
+    "additional_info": [
+        {
+            "url": "http://arxiv.org/abs/2404.15189v1",
+            "title": "Text2Grasp: Grasp synthesis by text prompts of object grasping parts",
+            "abstract": "The hand plays a pivotal role in human ability to grasp and manipulate\nobjects and controllable grasp synthesis is the key for successfully performing\ndownstream tasks. Existing methods that use human intention or task-level\nlanguage as control signals for grasping inherently face ambiguity. To address\nthis challenge, we propose a grasp synthesis method guided by text prompts of\nobject grasping parts, Text2Grasp, which provides more precise control.\nSpecifically, we present a two-stage method that includes a text-guided\ndiffusion model TextGraspDiff to first generate a coarse grasp pose, then apply\na hand-object contact optimization process to ensure both plausibility and\ndiversity. Furthermore, by leveraging Large Language Model, our method\nfacilitates grasp synthesis guided by task-level and personalized text\ndescriptions without additional manual annotations. Extensive experiments\ndemonstrate that our method achieves not only accurate part-level grasp control\nbut also comparable performance in grasp quality.",
+            "authors": "Xiaoyun Chang, Yi Sun",
+            "published": "2024-04-09",
+            "updated": "2024-04-09",
+            "primary_cat": "cs.AI",
+            "cats": [
+                "cs.AI"
+            ],
+            "label": "Original Paper",
+            "paper_cat": "Diffusion AND Model",
+            "gt": "Modeling hand grasps have recently gained extensive at- tention due to its wide applications in human-computer in- teraction [24], virtual reality [11, 39], and imitation learn- ing in robotics [12]. To predict plausible human-like grasp poses when given an object, many hand-object interac- tion datasets [4, 5, 8, 9] has been built to promote research [19, 20, 32] on learning human experience in recent years. However, these works concentrate on stable grasps that are not suitable for task-oriented grasps. Different tasks neces- sitate specific types of grasps. For instance, in a cutting task, people typically grasp a knife by its handle rather than the blade. Similarly, when handing over a knife, it is safer for the deliverer to hold the blade, minimizing the risk of injury to the receiver. Consequently, controllable grasp synthesis *cgsmalcloud83@mail.dlut.edu.cn \u2020Corresponding author, lslwf@dlut.edu.cn Input Output Input Output Template Text Personalized   Text  Task-level  Text Grasp the bar of the eyeglasses. Grasp the cap of the headphones. I want to drink using mug. Hold onto the  bottle\u2019s cap firmly. Seize the pen by its body. I want to cut apple using knife. Input Output Input Output Input Output Input Output Figure 1. Given an object, Text2Grasp can generate specific hand grasps by interpreting various text inputs: a) Template text. b) Personalized text. c) Task-level text. is of paramount important. To facilitate controllable synthesis, many studies [2, 14, 32, 41] introduce various datasets of grasp containing dif- ferent numbers of human intentions, such as use, pass, twist and so on. Furthermore, [41] and [14] translate these inten- tions into one-hot embeddings, combining them with object point cloud feature to achieve intention-guided grasp syn- thesis. Considering that language is more natural mode of interaction, some studies [23, 31, 34] start to employ task- level text descriptions as inputs for predicting 6-Dof pose of parallel jaw gripper. However, utilizing fixed set of in- tentions or task-level text descriptions for grasping inher- ently faces ambiguity, primarily in two aspects: 1) Same intention but different grasps. For instance, \u201dlifting a mug\u201d may involve different grasp types of either grasping the han- dle or the body. 2) Different intentions but same grasps. For instance, \u201dlifting\u201d or\u201d twisting\u201d might have same initial grasping pose to hold a bottle\u2019s neck. Such complexities arXiv:2404.15189v1  [cs.AI]  9 Apr 2024 increase the difficulty in annotating datasets and achieving model convergence. To overcome these limitations, we propose a grasp syn- thesis method abbreviated as Text2Grasp that is guided by text prompts of object grasping parts, rather than inten- tions or task descriptions that are unable to explicitly in- dicate which part of the object to grasp. Text2Grasp takes an object and a predefined text template: Grasp the [Ob- ject Part] of the [Object Category] as input, and generates a grasp pose targeting the specified part of the object for manipulation. This part-level guidance reduces uncertainty compared to intent-based or task-level guidance, facilitat- ing better convergence of the grasp generation network. Specifically, we present a two-stage method that includes a text-guided diffusion model TextGraspDiff to first gen- erate a coarse grasp pose, then apply a hand-object con- tact optimization process to ensure both plausibility and diversity. Unlike all-finger optimization approaches that prioritize maximum object-finger contact [5]\u2014resulting in mainly closed-finger grasps\u2014our optimization emphasizes optimizing contact between the fingers and the object part specified by text description. This strategy ensures physical realism, diversity in grasps, and alignment with text. Furthermore, the template representation of text prompts for the object grasping parts also supports grasp synthesis guided by task-level and personalized text prompts, since LLM [3] has been able to divide the task descriptions into several execution steps, including the parts of the object that should be grasped. Subsequently, our Text2Grasp can generate task-level grasps taking the inference results of LLM as input. Moreover, the utilization of LLM allows for the expansion of our designed text templates, enriching the training dataset for personalized text descriptions. In summary, our contributions are as follows: \u2022 We propose Text2Grasp, a grasp synthesis method guided by text prompts of object grasping parts, offering a more natural interaction and precise grasp control. \u2022 We introduce a two-stage method that includes a text- guided diffusion model TextGraspDiff to first generate a coarse grasp pose, then apply a hand-object contact opti- mization process to ensure both plausibility and diversity. \u2022 By leveraging LLM, our method facilitates grasp syn- thesis guided by task-level and personalized text descrip- tions without additional manual annotations. Extensive experiments on public datasets demonstrate that our method achieves not only accurate part-level grasp control but also comparable performance to state-of-the-art methods in terms of grasp quality.",
+            "main_content": "There has been a significant amount of research in the field of grasp synthesis. Here, we focus on realistic human grasp synthesis and review the most relevant works. Based on whether the grasp generation is controllable, we categorize the synthesis algorithms into two types: Uncontrolled Grasp Synthesis and Controllable Grasp Synthesis. Uncontrolled Grasp Synthesis. Uncontrolled grasp synthesis primarily aims to generate hand pose capable of stably grasp objects without considering subsequent tasks. A trend has emerged to develop deep learning solutions, driven by the introduction of large-scale datasets of handobject interactions [2,5,8,9,14,32,41]. These methods learn the latent distribution of hand-object contact information or hand parameters through generative models, including Generative Adversarial Network (GAN) [7] and Conditional Variational Auto-Encoder (CVAE) [30]. GanHand [5] initially predicts the optimal grasp type from a taxonomy of 33 classes, and then employs a discriminator and an optimization to get a refined grasp. Instead of predicting MANO [29] parameters directly, ContactDB [1] use thermal cameras to capture object contact maps that reflect the contact regions of an object post-grasping and utilizes GAN to learn their distribution, facilitating grasp synthesis. Comparing with GAN [7], CVAE [30] are more popular in hand grasp synthesis because of its simple structure and one-step sampling procedure. GrabNet [32] utilizes CVAE by conditioning on the Basis Point Set [25] of objects and samples from the low-dimensional space mapped through CVAE to generate hand grasps. Additionally, it incorporates a neural network to refine the coarse pose. This approach is also followed by Oakink [41] and AffordPose [14]. Grasp Field [17] and HALO [16] learn an implicit grasping field using CVAE as the hand representation to produce highfidelity hand surface. GraspTTA [15] exploits the contact map introduced by ContactDB [1] to refine the grasps generated by CVAE during reference. Contact2Grasp [19] learns the distribution of contact map for grasps by CVAE and then maps the contact to grasps. Moreover, ContactGen [20] introduces a three-component model to represent the contact of hand-object: the contact probability, the specific hand part making contact, and the orientation of the touch, and a sequential VAE is proposed to learn these aspects for grasp synthesis. Despite its simplicity and direct sampling process, CVAE often suffer from the posterior collapse [13,37,43]. This leads to less diverse outputs, including simplistic samples like a slightly closed hand shape. To mitigate this problem, SceneDiffuser [13], UGG [21] and DexDiffuser [38] employ a diffusion-based denoising process, ensuring diverse sample generation by gradually denoising, thus avoiding direct latent space mapping. These aforementioned methods are capable of generating stable grasps. However, these grasps might not be consistent with human manipulation habits, making them less appropriate for the tasks. Consequently, instead of solely relying on object shape as input, we incorporate the text prompts of object grasping parts into diffusion model for controllable grasp synthesis. Moreover, in contrast to methods that utilize global optimization [5, 32] to refine grasps, our work introduces an optimization based on finger perception and object part perception. This strategy not only ensures grasp stability but also maintains diversity. Controllable Grasp Synthesis. The capacity for controllable grasping is crucial as it represents the first step for manipulation. To facilitate controllable grasp synthesis, datasets [2, 14, 32, 41] encompass a range of human intentions for dexterous hand grasping. ContactPose [2] identifies two basic intentions: use and pass. Expanding on this, GrabNet [32] introduces lifting and off-hand passing. OakInk [41] goes further by incorporating intentions such as holding and receiving. AffordPose [14] elaborates on the use intention, creating hand-centric categories like twisting, pulling, handle grasping, among eight total intentions. Additionally, to generate intent-driven grasps, OakInk [41] and AffordPose [14] translate these intentions into word embeddings, combining them with object point cloud features as the condition of CVAE to produce matching grasp pose. Considering that language is one of the most natural forms of human interaction, some studies employ task-level text descriptions as inputs for predicting grasps with parallel jaw gripper. These methods initially construct extensive datasets of grasps that include task-level text descriptions. Based on these datasets, [31] and [33] adopt a generatethen-select methodology. It involves initially generating a number of poses for parallel jaw gripper, followed by a selection process guided by task-level text descriptions. In contrast, [34] and [23] directly predict the position of gripper on the input RGB image or object point cloud based on task-level text description guidance. Comparing to the simple closing of a gripper, the human hand, with its higher degree of freedom, must not only ensure stable grasping but also maintain the rationality of itself and interaction, making grasp synthesis for it more challenging. These methods, utilizing fixed set of intentions or tasklevel text descriptions for grasping, inherently face ambiguity, especially when defining intentions or tasks for identical parts of an object, such as a mug\u2019s handle and body. To address this, we develop a grasp synthesis method guided by text prompts of object grasping parts. Compared to the ambiguity of intentions or task-level guidance, partlevel guidance offers lower uncertainty, which facilitates the convergence of grasp synthesis networks. Furthermore, our method contrasts with those requiring manual labeling [23,31,33,34], by leveraging Large Language Model [3] to facilitate grasp synthesis guided by task-level and personalized text descriptions without additional manual labels. 3. Methods Our aim is to achieve controllable grasp synthesis when given an object\u2019s point cloud and a text prompt of object grasping part, ensuring the generated hand grasps stably hold the object while aligning with the input text. To this end, we introduce a two-stage method that includes a textguided diffusion model TextGraspDiff to first generate a coarse grasp pose, then apply a hand-object contact optimization process to ensure both plausibility and diversity. The overview of our method is illustrated in Fig. 2. In this section, we first present our semi-automated text generation method in 3.1. We then detail the text-guided conditional diffusion model-TextGraspDiff in 3.2, and the hand-object contact optimization in Section 3.3. 3.1. Semi-automatic Text Generation for Grasp The key idea behind Text2Grasp is to leverage text prompts of object grasping parts to control grasp synthesis. Instead of relying on extensive manual annotations, which are extremely labor-intensive and time-consuming, we design a semi-automatic approach to generate text prompts for existing hand grasp dataset, as illustrated in Fig. 2. First, we predefined the text template, i.e., Grasp the [Object Part] of the [Object Category]. The object category can be directly provided by existing datasets, while the object part corresponding to each grasp can be determined through computation. Specifically, given the point cloud of an object and the hand mesh grasping it, we first calculate the contact between the object and the hand, assigning a contact label to each point on the object. And the \u201cObject Part\u201d label for each grasp is determined by the object part with the most contact points. Finally, we can generate a text template for each grasp in the datasets. Furthermore, we leverage Large Language Model [3] with strong text comprehension capabilities to expand the template text, thereby generating more personalized text descriptions. For example, given the prompt \u201cPlease write [N] sentences with the same meanings as [template].\u201d, where N is the number of generated text descriptions, LLM can then infer a variety of plausible text descriptions to form our candidate text list L. During training, we randomly select one description from L as a training label for each grasp. This semi-automatic text generation approach facilitates personalized text inputs, thereby enhancing the flexibility of grasp synthesis control. In addition, the representation of the text prompts for the object grasping parts gives our method the ability to achieve task-level grasp synthesis because Large Language Model [3] can provide a description of the grasping action from a task description, such as grasping the mug\u2019s handle for drinking task. Thus we can accomplish task-level grasp synthesis without extra training. 3.2. Text to Grasp via Diffusion Model In this section, we introduce TextGraspDiff, a conditional diffusion model for grasp synthesis that is guided by Text \u201cGrasp the handle of the mug.\u201d Clip PointNet++ Diffuse  Process \ud835\udc54\ud835\udc61 Time Embedding \u2026 ResBlock Attention Conv \ud835\udc540 \ud835\udc61 Multi-Modal Attention \ud835\udc540 \ud835\udc54\ud835\udc61\u22121 Q K V \u2026 Denoising Network  G\uf071 Object Part Perception Finger Perception Text TextSegNet TextGraspDiff Optimization 1 1 1 0 0 Finger  Vector \ud835\udc5c Pose Shape HO_distance Finger Vector Grasp Vector steps \ud835\udc47 \ud835\udc59 Semi-automatic Text Generation Contact Points \u201cGrasp the  Part  of the  Object.\u201d Part Category Object Category Template Text LLM Prompt \u201cMore descriptions.\u201d Personalized Text \"1. Take hold of the mug's handle.\" \"2. Hold on the mug's handle firmly.\" \"3. Grip the handle of the mug.\" \u201c4. \u2026...\u201d \ud835\udc3f Figure 2. The Overview of Text2Grasp. We present a semi-automatic approach to generate both the template text and the personalized text prompts for each grasp in the datasets, which are used to train TexGraspDiff. And given the point cloud of object and text description of object grasping parts, we introduce a two-stage method that includes a text-guided diffusion model TextGraspDiff to first generate a coarse grasp pose, then apply a hand-object contact optimization process to ensure both plausibility and diversity. The final hand mesh can be obtained by MANO model [29]. text prompts of object grasping part. The overview of our method is illustrated in Fig. 2. Taking the object point cloud o \u2208RN\u00d73 and the part-level text prompts l, TextGraspDiff outputs a hand grasp vector g \u2208R66. This grasp vector encompasses MANO [29] model pose g\u03b8 \u2208R48, shape g\u03b2 \u2208R10, the distance gdis \u2208R3 between object and hand centroids, and the finger vector gf \u2208R5, which indicates which fingers are being used for grasping. Adhering to the diffusion model outlined in [10], our method is comprised of both a forward process and a reverse process. Forward process. Given a grasp vector g0, sampling from the ground-truth data distribution, we add the infinitesimal Gaussian noise \u03f5t \u223cN(0, \u03b2tI) into g0 and get a sequence of noised data {gi}T t=1 after T step. \u03b2t adheres to a linear variance schedule. q(gt | g0) = N(gt; \u221a\u00af \u03b1tg0, (1 \u2212\u00af \u03b1t)I) (1) where \u03b1t = 1 \u2212\u03b2t, \u03b1t = Qt s=1 \u03b1s. After T steps, if the amount of noise added is sufficiently large, then gT approximately converges to a standard Gaussian distribution. Reverse process. The process reverses noise sampled from a Gaussian distribution back into a sample from the data distribution for a fixed timestep. In our work, with the grasp vector g0 as the target for denoising process, and object point cloud o and its text prompt l of object grasping part as conditions, the conditional diffusion model leads to p(gt\u22121|gt, o, l). Following [27, 35], we predict the grasp vector g0 using a neural network G\u03b8. This process can be formalized as: p \u0000gt\u22121| gt, o, l \u0001 = N \u0012 gt\u22121; \u00b5\u03b8(gt, o, l, t), e \u03b2tI \u0013 (2) \u02dc \u00b5\u03b8(gt, o, l) = \u221a\u00af \u03b1t\u22121\u03b2t 1 \u2212\u03b1t G\u03b8(gt, o, l, t) + \u221a\u03b1t(1 \u2212\u03b1t\u22121) 1 \u2212\u03b1t gt (3) The detailed structure of the denoising network G\u03b8 is shown in Fig. 2, we employ a Transformer [36] as the denoising network\u2019s backbone, which has demonstrated promising results in human motion synthesis [27, 35] and robotic hand grasp synthesis [13, 21]. For multi-condition inputs, including point clouds and text, we initially employ the PointNet++ [26] and the pretrained CLIP [28] model as respective encoders to extract the point cloud feature and text feature. Instead of simply adding these multi-modal features, we design a Multi-Modal Attention Module based on Transformer [36] for effective fusion, leveraging point cloud feature fp as the query and text feature fl as the key and the value. This fusion mechanism enables us to achieve more precise control over grasp locations. Following [13], we incorporate a timestep-residual block and cross-attention for input noise embedding feature-condition fusion to ensure the network is effectively guided by step t and the condition c. Finally, the grasp vector g0 can be predicted by final output layer. The loss function of the network G\u03b8 is: L = Eg0\u223cq(g0|o,l),t\u223c[1,T ][\u2225g0 \u2212G\u03b8(gt, t, o, l)\u22252 2] (4) After completing the training of the denoising network G\u03b8 , when given a new object\u2019s point cloud and text description as conditions, we first sample random noise from a Gaussian distribution, then apply the denoising network G\u03b8 and Eq. (2) and Eq. (3) over T steps, and finally we obtain the grasp vector matching the object\u2019s part-level text description. The grasp hand mesh is then generated by applying the final grasp vector to the MANO model [29]. 3.3. Text-guided Contact Optimization To produce physically more plausible grasps, many works [5, 9, 15, 19] introduce a refinement stage to enhance contact and minimize penetration. Their main focus is on stable grasping by aligning hand with the closest object surface points, but these points may not match the text-described object parts, potentially leading to inaccurate grasp locations. Therefore, we propose a text-guided contact optimization method based on finger perception and text-guided object part perception. It guides specific fingers toward the object part described by text description, further enhancing grasp stability, diversity, and grasp part accuracy. Hand finger perception. Rather than minimizing the distance between all prior hand contact vertices often utilized for grasping and object points, we specifically optimize the distance between the object and the particular fingers used for grasping. We utilize a five-dimensional finger vector to define which fingers are used in grasping the object. For instance, as shown in Fig. 3, if the grasp involves using the thumb, index, and middle finger, then the finger vector gf is [1,1,1,0,0]. Following human habits, this vector is generated alongside the grasp. During optimization, we minimize the distance only between the object and those fingers indicated by a 1 in the finger vector, avoiding the issue of all fingers contacting the object. The loss for the finger perception optimization is formulated as: Hc = 5 [ i=1 {Ci | gi f = 1} (5) Lhc(Hc, O) = 1 | Hc | X h\u2208Hc min k \u2225h, Ok\u2225 (6) Optimization w/ finger perception  Optimization w/ object part perception  Figure 3. The Contact optimization. The contact optimization consists of finger perception and object part perception. The finger perception optimization directs the particular fingers used for grasping towards object and the object part optimization guided fingers toward the object part specified by text. where Ci represents the set of hand vertices which belongs to the ith fingertips, statistics by [9]. And Hc denotes the set of points for all fingers making contact. Text-guided object part perception. As shown in Fig. 3 we minimize the distance between hand contact points and object part specified by the text input to guide hand fingers to grasp the correct object part. Specifically, using a pretrained text-guided segmentation network TextSegNet, we first segment the input object point cloud into targeted Oc and non-targeted parts Onc based on the input text prompts of object grasping part. During the optimization, we assign higher weights to the targeted part, directing the hand contact points toward it to enhance the accuracy of the grasp part. The hand-object contact loss is formulated as follows: Lc(Hc, O) = \u03bb1Lnc(Hc, Oc) + \u03bb2Lnc(Hc, Onc) (7) where \u03bb1 and \u03bb2 are hyperparameters. Oc = {pi \u2208 O| Fseg(pi, l) = 1} and Onc = {pi \u2208O| Fgcd(pi, l) = 0} respectively represent the targeted and non-targeted parts. Fseg is the pretrained text-guided segmentation network TextSegNet. We also use PointNet++ [26] and CLIP [28] for point cloud and text encoding, followed by a multi-layer fully connected network to output segmentation labels. The training loss utilizes negative log-likelihood loss. Others. Following [5,9], we minimize the object points that are inside the hand distance to their closest hand surface points to penalize hand and object interpenetration by Lptr. Furthermore, following [44], we incorporate a joint angle limitation loss Langle and a self-collision loss Lself for the hand to ensure the plausibility of the grasping hand pose. Ultimately, our overall optimization objective is formulated as follows: min g\u03b8,g\u03b2,gdis \u03bbcLc+\u03bbptrLptr+\u03bbangleLangle+\u03bbselfLself (8) where \u03bbc , \u03bbptr , \u03bbangle and \u03bbself is a hyper-parameter. We utilize this objective function to optimize the networkpredicted MANO model pose g\u03b8 , shape g\u03b2, the distance gdis between object and hand centroids, aiming to further enhance the quality of generated grasps and the part accuracy of grasp . 4. Experiments In this section, we demonstrate the performance of our proposed PLAN-Grasp. We first introduce our implementation details in Sec. 4.1, followed by the used datasets and evaluation metrics in Sec. 4.2 and Sec. 4.3, respectively. In Sec. 4.4, we compare our method with the state-of-the-art methods and various applications that we can support. Finally, in Sec. 4.5, we conduct ablation studies to verify the effectiveness of components we design. 4.1. Implementation Details We conduct all the experiments using a single NVIDIA GeForce RTX4090 GPU with 24G memory. We sample N=2048 points sampling from the object surface as the input object points. During the training, we use the Adam optimizer [18] with the learning rate of 1e-4 to train the denoising network LAN-GraspDiff for 1000 epochs. The training batch size is 64. Following Scenediffuser [13], we set the diffusion step T to 100 , which is enough for a single 3D hand pose. During the refinement stage, we utilize Adamax [18] to optimize the grasp vector, applying different learning rates for its components: 1e-2 for hand pose, 1e-5 for hand shape, and 1e-4 for the distance between hand and object centroids, across a total of 200 epochs. 4.2. Dataset OakInk. The OakInk [41] is a large-scale dataset that captures hand-object interactions oriented around 5 intents: use, hold, lift-up, hand-out, and receive. It provides 1800 object models of 32 categories with their part labels and interacting hand poses. We use the shape-based subset OakShape to conduct experiments, 1308 objects for training and 183 objects for evaluation. AffordPose. The AffordPose [14] is a large dataset of hand-object interactions with 8 affordance-driven labels such as twist, lift, and press. It comprises 641 objects from 13 categories in PartNet [22] and PartNet-Mobility [40]. To evaluate the generalization ability of our method, we select 6 object categories identical to OakInk [41]: bottle, disperser, earphone, knife, mug and scissors, and randomly chose 30 instances from each category for testing. 4.3. Metrics A superior text-guided grasp should not only securely hold the object but also grasp the correct object part specified by text prompts. In this work, we adopt 4 metrics in total cover both grasp quality and grasp part accuracy. Penetration. Following [19, 41, 42], we compute the Penetration Depth and the Solid Intersection Volume between hand and object to measure the hand-object penetration. The PD is the maximum distance of all the penetrated hand vertices to their closet object surface, and the SIV is calculated by summing the volume of object voxels that are inside the hand surface. Simulation Displacement. Following [9, 20, 41], we place the object and the predicted hand into simulator [6], and calculate the displacement of the object center over a period of time by applying gravity to the object. Diversity. Following [16, 20], we measure the diversity by clustering generated grasps into 20 clusters using K-means, and calculate the entropy of the cluster assignments and the average cluster size. Grasp Part Accuracy. Employing the approach introduced in Sec. 3.2, we assign text template to each generated grasp and determine their accuracy by comparing with the input text descriptions. Grasp Part Accuracy is defined as the ratio of correctly identified grasps to the overall number of the generated grasps. 4.4. Comparison with the State-Of-The-Arts To evaluate the controllability of grasp synthesis in our method, we utilize two class-level public datasets, OakInk [41] and AffordPose [14], comprising multiple categories and instances within each category. Instance-level datasets like Grab [32] and HO3D [8] are unsuitable for evaluating our method because they contain only one instance per category, and only achieve controllability on a single instance cannot verify our generalization ability. For a fair comparison, we compare the state-of-the-art method trained on OakInk [41]: GrabNet [32], which is used for grasp generation in newest work [14, 41]. We train it on the OakInk dataset using its officially released code and test it and our method on 183 unseen objects from the OakInk dataset and 180 out-of-domain objects from the AffordPose dataset. Following [16,20], we generate 20 hand grasps for each test object. Specifically for our methods, we randomly create 20 text prompts based on the parts of each test object, using these prompts and the objects as inputs to produce grasps. We first present the quantitative comparison results on the in-domain OakInk [41] dataset and the out-of-domain AffordPose [14] dataset as shown in Tab. 1. It can be seen that our method achieves the lower penetration and simulation displacement on the OakInk dataset indicating the higher grasp quality than GrabNet [32]. Besides, our results are close to and even outperform the ground truth in diversity that demonstrate our method achieves more diverse and natural grasps. Experimental results on AffordPose [14] Dataset demonstrate that our method achieves the Dataset Methods Penetration Simulation Displacement Mean \u00b1 Var\u2193 Diversity Part Accuracy\u2191 Depth\u2193 Volume\u2193 Entropy\u2191 Cluster Size\u2191 OakInk TestGT 0.11 0.65 1.80 \u00b1 2.04 2.91 4.11 100.00 GrabNet [32] 0.48 2.97 2.84 \u00b1 2.81 2.95 2.57 Ourstemplate 0.40 1.89 2.49 \u00b1 2.51 2.92 4.70 87.76 Ourspersonalized 0.41 1.73 2.49 \u00b1 2.57 2.92 4.74 82.32 AffordPose GrabNet [32] 0.54 3.77 3.09 \u00b1 2.74 2.94 2.52 Ourstemplate 0.66 5.05 2.93 \u00b1 2.67 2.90 4.88 78.53 Ourspersonalized 0.59 3.84 3.00 \u00b1 2.86 2.87 4.79 73.83 Table 1. The quantitative results on the OakInk [41] dataset and the AffordPose [14] dataset.TestGT means the grouth-truth grasps on the OakInk Test datasets. Ourstemplate and Ourspersonalized refer to the grasps generated when using template and personalized text description inputs, respectively. \u2191denotes higher values are better, \u2193denotes lower values are better. Ours GrabNet GrabNet Ours Figure 4. The qualitative results on the OakInk [41] dataset and the AffordPose [14] dataset. The results demonstrated above the dotted line are from OakInk [41] dataset, while below are from AffordPose [14] dataset. comparable generalization ability, with the lower simulation displacement, higher diversity, and comparable penetration. More importantly, we achieve the grasp controllability by text prompts of object grasping parts, a capability not present in GrabNet [32] and get grasp part accuracy of 87.76% with template text and 82.32% with personalized text on OakInk dataset [41] as shown in Tab. 1. Furthermore, to evaluate the performance qualitatively, we visualize the generated hand grasps for both in-domain and out-of-domain objects by GrabNet [32] and our method. As shown in Fig. 4, it can be seen that both methods can generate plausible hand grasps for object part with sample shapes such as the body of mug and the cap of earphones. But for specific-part grasp such as the cap of bottle, we can observe clearly from the red boxes that the grasps our method generated has the smaller penetration and more natural contact. These results demonstrate our method\u2019s capability to generate physically plausible and stable grasp. Moreover, we visualize the multi-grasps for each object in Fig. 5. In contrast to the predominantly closed hand poses with five fingers generated by GrabNet [32], ours is better suitable for the specific shape of the object, as demonstrated Fig. 5 with the eyeglasses and knife. To show our grasp controllability, we visualize the results of grasp synthesis guided by text prompts of object grasping parts. which consist of template and personalized Ours GrabNet Input eyeglasses headphones scissors bottle knife Figure 5. The qualitative results of the diverse grasps on the objects. For each object, we visualize five grasps and the red shape represents abnormal grasps. Grasp the cap of the  cylinder bottle. Grasp the bridge of  the eyeglasses. Grasp the trigger of  the trigger sprayer. Grasp the head of  the pen. Grasp the handle of  the mug. Grasp the handle of  the screwdriver. Grasp the handle of  the fryingpan. Grasp the headband  of the headphones. Grasp the lotion  pump around its head. Clasp the bottle's  cylindrical body firmly. Hold the knife\u2018s  cutting edge. Pinch the cap of the  bottle. Hold onto the  eyeglasses' frame. Seize the panel of the  game controller. Take hold of the  wineglass's stem. Wrap your fingers around  the knife's handle. Figure 6. Visualization of the grasps generated when using different types of text inputs. The top row displays grasps produced from template text inputs, while the bottom row exhibits those generated from personalized text inputs. text descriptions. As shown in Fig. 6, our method not only generates hand poses that grasp the objects of different categories in a manner consistent with human habits but also directly produces grasps in a text-controlled manner. This level of controllability enables precise object part grasping for subsequent tasks. 4.5. Ablation Study VAE vs Diffusion. To fairly evaluate the effectiveness of the diffusion model we employed, we construct a variant of our method by replace the diffusion model with VAE for part-level grasp sythesis. Both this model and ours remove the optimization process. The results on the OakInk [41] dataset are shown in the first two rows of Tab. 2 and Fig. 7. From the experimental results we can see diffusion model achieves the higher grasp quality with lower penetration and higher grasp part accuracy. More importantly, it can be seen obviously from Fig. 7 that our diffusion model can generate more diverse hand pose for mug and bottle than VAE. Multi-Modal Attention. We evaluate the effectiveness of the Multi-Modal Attention which is designed to fuse the text feature and the object point feature. Specifically, we compare this module with feature addition. As shown in the 3rd and the 4th of Tab. 2, the multi-modal attention outperforms feature addition across all metrics, especially in the grasp part accuracy. Optimiziation. We evaluate the effectiveness of optimization based on finger perception and text-guided object part perception, and the results are shown in Tab. 2 and Fig. 8. Note that here we use Baseline (Base.) to represent Methods Penetration Simulation Displacement Mean \u00b1 Var\u2193 Diversity Part Accuracy\u2191 Depth\u2193 Volume\u2193 Entropy\u2191 Cluster Size\u2191 Base.(VAE) 0.55 8.44 2.48\u00b12.56 2.90 3.15 77.38 Base. (Diffusion) 0.38 2.82 3.00\u00b13.04 2.93 3.46 85.25 Base. w/ Add fusion 0.38 2.89 3.09\u00b12.92 2.90 3.45 83.44 Base. w/ Attention fusion 0.38 2.82 3.00\u00b13.04 2.93 3.46 85.25 Base. (Diffusion) 0.38 2.82 3.00\u00b13.04 2.93 3.46 85.25 Base. + opt. w/ global 0.39 1.82 2.39\u00b12.34 2.95 4.18 83.69 Base. + opt. w/ finger perception 0.38 1.79 2.50\u00b12.56 2.95 4.41 83.74 Base. + opt. w/ finger perception and object part perception 0.40 1.89 2.49\u00b12.51 2.92 4.70 87.76 Base. + opt. w/ refinenet [32] 0.30 1.38 3.11\u00b12.81 2.87 2.86 83.55 Table 2. The quantitative results of ablation study on the OakInk [41] dataset. \u2191denotes higher values are better, \u2193denotes lower values are better. Base. (VAE) Base. (Diffusion) Figure 7. Comparisons of ours based on VAE(Base. (VAE)) and diffusion model (Base. (Diffusion)). Baseline Opt. w/o finger perception Opt. w/ finger perception Baseline Opt. w/o part perception Opt. w/  Refinenet[] Opt. w/  Refinenet[] Opt. w/ part perception Figure 8. Comparisons of different optimization strategies. Figure 9. Visualization of the grasps generated from the text input \u2019grasp the handle of the faucet\u2019 given an unseen category faucet. our method without any optimization. It can be seen the grasp quality achieves a significant improvement by adding the global optimization which leads all-fingers toward object for Baseline. Specifically, the penetration volume and the simulation displacement have decreased by 35.46%, and 20.33% respectively, while diversity has improving by 20.81%. However, it directs all fingers towards the object\u2019s nearest point, limiting the diversity and leading to inaccuracies in the contact part, as shown in Fig. 8. In contrast, our optimization, grounded in finger perception, fine-tunes only the fingers involved in grasping, while the rest maintain a natural state. This approach enables us to maintain grasp quality while achieving greater diversity. Furthermore, as shown in Fig. 8, the optimization based on text-guided object part perception focuses on directly the hand towards the part described by text description, enabling us to achieve a higher grasp part accuracy. In addition, we compare our optimization with the RefineNet used by GrabNet [32]. It is trained to denoise on the dataset built by adding random noise into ground-truth hand-object interaction. As the Fig. 8 illustrated, grasps optimized by RefineNet still do not fully contact the blade. In contrast, our method, optimized for specific situations, performs better in detail. And the quantitative results in Tab. 2 demonstrate our methods achieve better balance between penetration and simulation displacement. 5. Discussion The part control ability of our method can be easily transferred among the objects in the seen categories. However, due to the limited categories in the training dataset, when faced with the objects of new categories that have never been seen in the training dataset, although reasonable grasp can be generated, the contact parts can not be identified because of the lack of understanding of the new categories. As shown in Fig. 9, our method can produce a reasonable grasp for the faucet but cannot accurately grasp the faucet\u2019s handle. Therefore, it is necessary to train on a grasp dataset with more categories, but such a dataset is currently not available. In addition, with the help of the Large Language Models [3], we can achieve task-level static grasp synthesis, such as grasp the handle of the knife rather than the blade when cutting fruit. However, correctly grasping the part of an object is the first step to complete the task and the ability to dynamically manipulate objects is also the key for task. We will do more exploration in the future. 6. Conclusion In this work, we introduce Text2Grasp, a grasp synthesis method guided by text prompts of object grasping parts. It begins with a text-guided diffusion model, termed TextGraspDiff, which is responsible for generating an initial, coarse grasp pose. This is subsequently refined through a hand-object contact optimization process. This method ensures that the generated grasps are not only physically plausible and diverse but also precisely aimed at specific object parts described by text prompts. Furthermore, our method also supports grasp synthesis guided by personalized text and task-level text descriptions by LLM without extra manual annotations. Extensive experiments conducted on two public datasets demonstrate our methods achieves not only the comparable performance in grasp quality but also precise part-level grasp control."
+        },
+        {
+            "url": "http://arxiv.org/abs/2404.05519v1",
+            "title": "Investigating the Effectiveness of Cross-Attention to Unlock Zero-Shot Editing of Text-to-Video Diffusion Models",
+            "abstract": "With recent advances in image and video diffusion models for content\ncreation, a plethora of techniques have been proposed for customizing their\ngenerated content. In particular, manipulating the cross-attention layers of\nText-to-Image (T2I) diffusion models has shown great promise in controlling the\nshape and location of objects in the scene. Transferring image-editing\ntechniques to the video domain, however, is extremely challenging as object\nmotion and temporal consistency are difficult to capture accurately. In this\nwork, we take a first look at the role of cross-attention in Text-to-Video\n(T2V) diffusion models for zero-shot video editing. While one-shot models have\nshown potential in controlling motion and camera movement, we demonstrate\nzero-shot control over object shape, position and movement in T2V models. We\nshow that despite the limitations of current T2V models, cross-attention\nguidance can be a promising approach for editing videos.",
+            "authors": "Saman Motamed, Wouter Van Gansbeke, Luc Van Gool",
+            "published": "2024-04-08",
+            "updated": "2024-04-08",
+            "primary_cat": "cs.CV",
+            "cats": [
+                "cs.CV",
+                "cs.LG"
+            ],
+            "label": "Original Paper",
+            "paper_cat": "Diffusion AND Model",
+            "gt": "Text-to-Video diffusion models [2, 3, 18, 41, 46] have been fast advancing in generating temporally consistent scenes with plausible object interactions. There has been a series of works that have focused on editing T2V models to enable greater control over video generation. More successful edit- ing methods have made use of small sets of reference videos to learn an object\u2019s motion or camera movement. They sub- sequently transfer that specific movement or camera motion to a new object and scene [21, 52, 56] by training parts of the video diffusion model or performing Low Rank Adap- tation (LoRA) [19]. While these methods can be effective, they require additional data and compute with limited flex- ibility, which limits their adoption in practice. Several works [40, 45, 47, 49] have shown the promise of attention maps in object discovery and segmentation. In the domain of text-to-image models, cross-attention and its role in controlling the scene layout has also been well studied. In particular, cross-attention is responsible for determining the objects\u2019 shape and size in the image. Cross-attention fa- cilitates maintaining semantic consistency between the text and the generated image. By attending to relevant textual features, the model ensures that the generated visual con- tent aligns with the overall semantics of the input descrip- tion. One of the works that exploited cross-attentions to enable editing images was Prompt-to-Prompt [16]. This work showed that the shape of an object a can be replaced with the shape of another object b by replacing a\u2019s cross- attentions with those of b. Training-Free Layout Control [7] was another work that proposed an energy-based ob- jective to control the position of objects in the generated image. Given a user-specified bounding box, the energy function encourages the cross-attention maps of a token to form within the bounding box and hence position the ob- ject within the bounding box. Diffusion self-guidance [12] generalized the Training-Free Layout Control method such that editing the scene could be done by using the cross- attention maps alone, without the need for external inputs (e.g., bounding box), in a zero-shot manner. This was achieved by applying transformations (e.g., relocating and resizing) to the original cross-attentions of a token and using the resulting cross-attentions as the target of the objective. With the success of the above methods for editing im- ages generated by T2I models [5, 12, 16, 30] or adapting T2I models for video editing [27], we ask the question; \u201cDo such approaches for editing images transfer to the video do- main?\u201d. In particular, we are interested in exploring the ef- fectiveness of cross-attention layers for editing the subject\u2019s size, positioning, and motion in videos. In this paper, we build upon the achievements of prior image-editing techniques by extending them to the video domain. More specifically, our contributions are threefold: \u2022 We take a first look at cross-attention layers in T2V dif- fusion models and their role in editing videos. \u2022 We explore two possible ways to use cross-attentions in editing videos; namely forward and backward guidance. arXiv:2404.05519v1  [cs.CV]  8 Apr 2024 Figure 1. This figure shows an overview of backward guidance in T2V models. On the left, we show the generated frames of the T2V model after t steps, given an initial input latent zt and the text prompt \u201cA burger floats on the water\u201d. To edit the video and move the burger from the top-left of the screen to the bottom-left in a straight line, we generate Atarfi for each frame fi reflecting this edit. Following the scheme in Section 4.2, we update the latent through the denoising process based on objective E. At time step 0, z0 generates the video on the right which reflects the intended edit. \u2022 We investigate the limitations of current T2V models that hinder the capabilities of video editing methods.",
+            "main_content": "Denoising Diffusion Models. The denoising diffusion paradigm [1, 42, 43] emerged as a new method to generate images with high photo-realism and diversity. It has rapidly advanced text-conditioned image generation [11, 14, 17, 31, 34\u201336, 39, 54, 55], which is important for gaining control over its generated content. Due to their versatility and representation learning capabilities [8, 20, 53], they have also been successfully adapted for specialized tasks such as classification [10, 26], depth prediction [23] and segmentation [6, 22, 44]. Personalizing Image Generation. Personalizing [13, 25, 29, 38, 50, 55] and editing [5, 12, 16, 30, 32] T2I models Personalizing Image Generation. Personalizing [13, 25, 29, 38, 50, 55] and editing [5, 12, 16, 30, 32] T2I models has become a research focus to enable user-intuitive control for creating content with these generative models. In particular, the cross-attention layers of diffusion models have been studied for their role in determining a scene\u2019s layout and their ability to enable zero-shot editing of generated images. Similar to [5], we split cross-attention-based editing of T2I and T2V models into two categories of 1) forward and 2) backward guidance. In forward guidance, cross-attention manipulation occurs directly during the denoising process via a forward pass through the model. A notable example of forward guidance is Prompt-to-Prompt [16], which proposes replacing the token\u2019s cross-attentions from a source prompt with those of a target prompt. Figure 2 shows one such example in the video domain where the cross-attentions of \u201ccar\u201d, from the source prompt \u201ccar drives on the road\u201d, are replaced with cross-attentions of \u201ctruck\u201d, from the target prompt \u201ctruck drives on the road\u201d. To enable more precise modifications to a specific source token, while preserving the overall scene, forward guidance requires source and target prompts that differ by a single token, limiting its applicability. In contrast to forward guidance that directly manipulates cross-attentions, backward guidance biases the crossattention through backpropagation. By designing an energy-based loss that encourages some desired edit [5, 12], the gradient of the loss is then used to update the input latent zt of the model. Training-Free Layout Control [5] is an example of backward guidance where the energy function encourages the cross-attentions of the user-specified token to obtain higher values inside a user-defined bounding box. At multiple time steps, the input latent is updated to realize this objective. Similarly, Diffusion self-guidance [12] designed energy functions that encourage the cross-attentions to take certain shapes or positions within the image. This paper is inspired by the success of these two works in the image domain. In Section 3.3, we show that forward guidance is too restrictive to enable effective video editing. In Section 3.4, we show backward guidance\u2019s promise in enabling zero-shot editing of T2V models. Text-to-Video Generation. Diffusion models have been improving at high-quality video generation by training conditional denoising networks (e.g, 3D U-Net [9], DiT [33]) to denoise randomly sampled sequences of Gaussian noises [2, 3, 18, 28, 41, 46]. Some works take advantage of large, pre-trained text-to-image foundation models to build textto-video models. This is done by inflating the T2I model with temporal layers, like Tune-A-Video [51], Text2VideoZero [24] and AnimateDiff [15]. Personalizing Video Generation. Following the same desire to control image generation, a few works focused on video editing and customizing the motion and camera movement in T2V models [7, 21, 48, 52, 56]. Most current editing and customization methods work by tuning parts of the network or performing LoRA [19] based on example videos containing the desired effect. Such methods lack the flexibility of a zero-shot approach and require additional training data and resources. For this reason, we investigate the effectiveness of forward and backward guidance using cross-attention for T2V models. 3. Method 3.1. How Do Video Diffusion Models Work? Video diffusion models train a 3D denoising network, traditionally U-Nets but more recently transformer-based [33] networks, to generate videos from randomly sampled Gaussian noise. In this work, we use T2V models with 3D UNet backbone [46] which consists of down-blocks, middleblocks, and up-blocks. Each block has several convolution layers, spatial transformers, and temporal transformers. During training on videos, the U-Net (\u03f5\u03b8) and a text encoder (\u03c4\u03b8) are optimized with the following objective: L = Ez0,y,\u03f5\u223cN (0,I),t\u223cU(0,T ) = \u2225\u03f5 \u2212\u03f5\u03b8(zt, t, \u03c4\u03b8(y))\u22252 2, (1) where z0 \u2208Rf\u00d7b\u00d7h\u00d7w\u00d7c is the initial latent input of the training videos (b indicates the batch size, f is the number of frames, h, w and c are the height and width and channels respectively) and y is the text description of the video, with \u03f5 and t being the added Gaussian noise to the videos and the time step. At time step t, the noised latent is defined as: zt = \u221a\u00af \u03b1tz0 + \u221a 1 \u2212\u00af \u03b1t\u03f5, (2) where \u03b1t controls the noise strength. 3.2. T2V Cross-attention The cross-attention mechanism in the spatial transformers of the 3D U-Net enables the model to capture spatial relationships between the video frames and the input text. In this work, we focus on changing an object\u2019s size, location and motion given a latent input and text prompt to the T2V model. To this end, we work with the cross-attention layers of the 3D U-Net where {Ai,t,.,.,k \u2208RHi\u00d7Wi\u00d7|k|} is the Softmax-normalized cross-attention map of the ith layer of the U-Net, at time step t for token k. 3.3. Forward T2V Guidance Following the works that perform forward guidance in T2I models [4, 16, 32], we implemented forward guidance in the T2V pipeline. Figure 2 is one example where the crossattentions of \u201ccar\u201d are replaced with the cross-attentions of \u201ctruck\u201d. Below are the two main limitations with forward guidance that have also been observed in the T2I domain. \u2022 Size and Shape Mismatch. Forward guidance is restrictive and can lead to artifacts due to the difference in shape and size of the two objects. In the example of Figure 2, since the truck is larger than the car, injecting the cross-attentions of the truck to replace the car\u2019s has led to artifacts around the car without changing the car\u2019s size to match the truck\u2019s. \u2022 Cross-attention Overlap. The cross-attentions of different tokens can overlap. We refer to the top row of Figure 3, where the shark is still visible in the crossattention maps of tokens \u201cin\u201d and \u201cthe\u201d. For this reason, forward guidance can work reasonably well where the two source and target sentences only differ by one token (i.e., Prompt-to-Prompt\u2019s setting). This overlap can cause degradation in the image and video quality, especially when the text inputs differ by more than one token. We note that some of these artifacts are due to the current T2V models generating noisy cross-attentions. We go over more details in Section 4.1 regarding this limitation. 3.4. Backward T2V Guidance Following Diffusion self-guidance [12] and Training-Free Layout Control [5], we define an energy function E to encourage specific shape, size and motion properties on the cross-attentions of some user-specified token k. Figure 1 gives an overview of our backward guidance where Aorigfi is the cross-attention map of some user-specified token k (e.g., token corresponding to \u201cburger\u201d) in frame fi of the video generated by the T2V model. we omit the layer number and the token k in our notation of the cross-attention. Atarfi is the target cross-attention that captures the properties of the editing task. In Figure 1, the task is to move the burger from the top-left to the bottom-left of the scene. We Figure 2. We show an example of forward guidance by swapping the cross-attention maps of \u201ccar\u201d with cross-attention maps of the \u201ctruck\u201d. The two input texts only differ in one token (\u201ctruck\u201d and \u201ccar\u201d). While the car follows the motion and location of the truck in the video, artifacts can be seen around the car due to the mismatch in size and shape of the truck and car. Figure 3. We compare the cross-attention maps for the same prompt to a T2I and T2V model. The cross-attention maps are extracted and averaged at the 16 \u00d7 16 resolution from the mid-blocks and up-blocks of the U-Net. Open-source T2I models currently produce much less noisy cross-attention maps compared to T2V models. In Section 4.1, we give details on how the noisy cross-attentions hinder backward guidance and propose a procedure for bypassing this limitation for our experiments in this paper. define the energy function E below. To control the shape and size of an object (indicated by token k) through its corresponding cross-attention maps, we threshold the attention map to eliminate the effect of background noise and overlapping attention from other tokens. This is achieved by taking a soft threshold at the midpoint of the per-channel minimum and maximum values: shape(k) = Athreshold k . Using the thresholded original cross-attention and the target cross-attention, we define the energy function E as: E = shape(Atar) \u2212shape(Aorig). (3) This objective is zero-shot since shape(Atar) can be computed as (M \u00d7 shape(Aorig)) where M defines some transformation such as resizing and relocating the original attention. At time step t, we update the latent zt according to the gradient of the loss defined by the energy function E. This is realized through the following equation: zt \u2190zt \u2212\u03b42 t \u03b7\u2207Zt X E(Atar, Aorig), (4) where \u03b7 > 0 controls the strength of backward guidance and \u03b4t = p (1 \u2212\u03b1t)/\u03b1t. Updating the latent z in this manner indirectly influences the cross-attentions. Please refer to Section 4.2 for more details on our experimental setup. 4. Experiments 4.1. Limitation of Current T2V Models In Figure 3, we visualize the cross-attention maps for all tokens of the prompt \u201ca shark swims in the ocean\u201d generated with Stable Diffusion [37] and our T2V model [46]. Figure 4. We show qualitative results for shrinking and enlarging objects through backward guidance. The middle image of each row visualizes the first frame of the original video. We enlarge and shrink the target cross-attentions at four different levels (Big / Bigger and small / smaller) and update the latent through backward guidance. The first frame for each edited video is shown. The cross-attention maps in T2I models capture the tokens much better than T2V models. We attribute this to deeper denoising networks of T2I models, larger training datasets, and more cross-attention layers. Using such noisy cross-attention maps hinders both forward and backward guidance. To perform backward guidance more effectively, we opted to directly generate shape(Atar) for each frame. Instead of transforming shape(Aorig) to calculate shape(Atar) for each video frame, we generate binary cross-attention maps for the token of interest. Despite this backward guidance setup not being zero-shot, we rely on future T2V models with better cross-attention maps to replace this manual effort. Figure 1 shows an example of user-generated target cross-attentions. In this example, instead of transforming the cross-attention maps of the \u201cburger\u201d to calculate the target, we directly generate each frame\u2019s cross-attention according to our editing task. Here, the task is to move the burger from the top-left of the scene to the bottom-left in a straight line. Hence, we generate cross-attention maps for each frame. For frame 1, Atarf1 is placed at the top-left of the scene and in the following frames, the cross-attention map moves slightly down such that in the last frame, Atarf16 is placed at the bottom-left. 4.2. Experiment Details We use the ModelScope [46] T2V model in our experiments and generate 16 frame videos with 256\u00d7256 resolution. Image editing methods such as Diffusion self-guidance [12] have used the extracted image features learned by the denoising network to preserve the background details and appearance features of the object being edited. In this work, we only focus on controlling objects\u2019 motion and size and leave background and appearance consistency for future works. We experimented with text prompts that describe a simple scene, to further control the limitation of current T2V models and get less noisy cross-attention maps for the object we want to edit. Our 3D U-Net has cross-attentions with resolutions 4\u00d74, 8 \u00d7 8 , 16 \u00d7 16 and 32 \u00d7 32. We find the 8 \u00d7 8 and 16 \u00d7 16 cross-attentions to be the most important dimensions for effectively minimizing the energy function and editing the scene. There are 10 such layers in the down-blocks, midblocks, and up-blocks of the 3D U-Net (4 down-block, 2 mid-block, and 4 up-block layers). We found that midblock\u2019s cross-attentions played a vital role in backward guidance. Excluding the two mid-block layers resulted in failed edits whereas excluding either all of down-block\u2019s or all of up-block\u2019s cross-attentions resulted in fewer failures. We experimented with different schemes for updating the latent z and found the most effective strategy to be that of Diffusion self-guidance [12]. During the first N/4 iterations, we update z at each step. For the subsequent 3N/4 iterations, we update z at every other step. The guidance scale \u03b7 (eq. 4) also plays an important role in the method\u2019s effectiveness. Increasing \u03b7 too much leads to degradation in the generated frames. Selecting a very low scale does not change the latent enough for effective editing. We found that in our setting, a scale of 15 < \u03b7 < 25 provided a good balance between guidance strength and synthesis quality. 5. Results In this section, we show the capabilities of backward guidance for two different tasks. Figure 4 shows qualitative results for changing an object\u2019s size through backward guidance. Figure 5 presents qualitative results of backward guidance for controlling the motion of an object in a video. To edit an object of interest, we generate binary cross-attention maps that capture the target position for the object\u2019s token. For \u201cburger\u201d, we placed the first cross-attention at the topleft of the scene and slowly moved it down. For the \u201cball\u201d, we placed the cross-attention at the top-left and moved it towards the bottom-right of the scene. Finally, we moved the \u201cshark\u201d from the top-right towards the bottom-left of the scene. Each sequence of frames with the black caption shows the original video without performing guidance. The sequence of frames with blue instruction shows the video after updating the latent with backward guidance. The object successfully follows the cross-attention at each frame. We also observe that the original video can be missing an object described in the text. The example with prompt \u201cA wolf howls to the moon\u201d in Figure 5 is missing the moon. Interestingly, backward guidance encourages the moon to be present in the scene. Attend-and-Excite [4] achieves the same objective in the T2I domain. 6. Observations In this section, we go over a few interesting observations when experimenting with backward guidance. Perspective. In our experiments, we used a fixed size for Atar for all 16 video frames. However, if the object is moving away or toward the camera, we should see a change in the object\u2019s size. In Figure 5, we see the burger, ball, and shark getting larger as they move closer to the camera while the moon remains the same size as it is static in the sky. It is noteworthy that despite updating the model\u2019s input latent with fixed-size target cross-attentions, the model consistently generates videos with reasonable perspective. However, this comes at the expense of not strictly adhering to the exact size defined by Atar. Motion Control. To control the motion of objects, we interpolate the cross-attention maps between the attention map Atarf1, placed at starting position a and the attention map of the last frame Atarf16 placed in final position b. We observed that the model keeps the temporal consistency at the expense of not following the exact start and end location defined by the target cross-attention. For instance, in Figure 5 last row, we placed the cross-attention of the \u201cshark\u201d at the top-right for the first frame and at the bottom-left for the last (16th) frame. However, after t steps, the shark is not at the bottom of the scene where Atarf16 was positioned. To do so, the model needs to move the shark much faster to go from Atarf1 to Atarf16 in a short number of frames. We also note that compared to resizing an object, controlling its motion is often prone to failures using backward guidance. This failure takes the form of the object being statically positioned at Atarf1. We leave further exploration of this mode of failure for future work. 7. Discussion This study conducted an initial investigation into the significance of cross-attention layers within the 3D U-Net framework of video diffusion models. More specifically, focusing on their role in determining objects\u2019 size, position and motion in T2V models. We examined the efficacy of utilizing cross-attention maps to manipulate object size and motion, employing both forward and backward guidance. In Section 3.3, we showed that forward guidance in videos faces the same limitations that were previously observed in the T2I domain [7] which hinders its performance. In Section 5, we showed results for editing the size and motion of an object through backward guidance. Our findings emphasize the promise of backward guidance in enabling zeroshot editing capabilities for video generation. Moreover, in Section 4.1, we highlighted current limitations that impede the transition of cross-attention-based editing methods from the image domain to videos. This analysis provides insights into the challenges and opportunities inherent to adapting editing techniques to be used in dynamic video content. 8. Impact and Future Directions Enabling zero-shot editing capabilities for generative video models is a valuable approach to enhance user control without the need for model fine-tuning with additional data. While current video models face limitations in quality, length, and cross-attention accuracy, we anticipate that editing methodologies like ours will leverage future advancements in Text-to-Video models, similar to the progress seen in the Text-to-Image domain. In this study, we focused on manipulating objects\u2019 size and motion with backward guidance. However, practical applications for editing tools require further exploration, particularly enabling editing of real videos. This needs additional constraints such as controlling background alterations and maintaining the fidelity of different objects to the original video. These aspects remain open for future work. Figure 5. The figure visualizes the results of backward cross-attention guidance. For each of the 4 examples, we show the output of the T2V model given the prompt in black. The blue text describes the applied transformation to the cross-attentions at each frame. We update the input latent accordingly. The red bounding box highlights the edit\u2019s success."
+        },
+        {
+            "url": "http://arxiv.org/abs/2404.12227v1",
+            "title": "A Photoionization model for the Infrared Coronal Line Emission in the Classical Nova V1716 Scorpii",
+            "abstract": "A near-infrared spectrum of nova V1716 Scorpii (PNV J17224490-4137160), a\nrecent bright (V_max = 7.3 mag), Fermi-LAT detected gamma-ray source, was\nmodeled using the photoionization code CLOUDY. Abundances were estimated for\nHe, C, N, O, Si, Al, Mg, Fe, Ne, S, Ca, and P. Notably, P (a factor of 120) and\nN (a factor of 248) are highly overabundant. It was necessary to assume the\nejecta consist of two components (with a cylindrical geometry): a dense\ncomponent from which the bulk of the H, He, and neutral O~I and N emission\narises and a more diffuse component from which most of the coronal lines arise.\nSome of the coronal lines are found to originate from both the dense and\ndiffuse components. The mass of the ejecta, including neutral and ionized gas,\nis ~ 4.19e-4 solar masses. Our analysis indicates that in the case of V1716 Sco\n(which has a carbon-oxygen white dwarf), a fraction of 25% white dwarf matter\nrather than 50% is favored for the mixing between white dwarf and the accreted\nenvelope before the outburst. This mixing ratio is like that found for\nOxygen-Neon novae where a 25% mixing fraction is also indicated. Helium hydride\n-- the first molecule to form after the Big Bang -- may have formed in the\nejecta of V1716 Sco based on photoionization modeling. This prediction suggests\nthat novae may be potential formation sites of this important molecular ion.",
+            "authors": "C. E. Woodward, G. Shaw, S. Starrfield, A. Evans, K. L. Page",
+            "published": "2024-04-18",
+            "updated": "2024-04-18",
+            "primary_cat": "astro-ph.SR",
+            "cats": [
+                "astro-ph.SR"
+            ],
+            "label": "Original Paper",
+            "paper_cat": "Diffusion AND Model",
+            "gt": "1.",
+            "main_content": "Corresponding author: C.E. Woodward mailto:chickw024@gmail.com 3 \u2020 Visiting Astronomer at the Infrared Telescope Facility, which is operated by the University of Hawaii under contract 80HQTR19D0030 with the National Aeronautics and Space Administration. at several 100 to > \u223c1000 km s\u22121 (e.g., Bode & Evans 2012; Anupama & Kamath 2012). In view of the Galactic CN rate \u223c Anupama & Kamath 2012). In view of the Galactic CN rate (\u224347 yr\u22121; De et al. 2021), likely CNe are a major source of 13C, 15N and 17O in the Galaxy (Gehrz et al. 1998; Bode & Evans 2012) and may make a significant contribution to Galactic 7Li (Starrfield et al. 2020, 2024), although the case for this rests on observational results and not theory (Jos\u00b4 e et al. 2020; Kemp et al. 2022; Molaro et al. 2022, 2023). As the ejecta disperse, an emission line spectrum is produced and stable nuclear burning causes the pseudophotosphere to shrink, revealing a hotter, deeper source of emission. CNe spectra are remarkable for their changing elemental and ion content and the temporal development of line profiles is critical to understanding the dynamics of ejection. Low-energy permitted lines of CNO and Fe II give way to He II, as well as high ionization lines, e.g., [Fe VII] 6087 \u02da A, and ultimately to infrared (IR) \u201ccoronal\u201d lines (Raj et al. 2015; arXiv:2404.12227v1  [astro-ph.SR]  18 Apr 2024 2 WOODWARD ET AL. Woodward et al. 2021; Kumar et al. 2022). The latter lines are sources of abundance information as a wide range of isoelectronic sequences (Greenhouse et al. 1990) and adjacent ionization states of metals are observable. Often, as the ejecta cool and evolve, molecules (e.g., CO \u2013 Rudy et al. 2003; Pontefract & Rawlings 2004; Das et al. 2009; Banerjee et al. 2016) and dust form. CNe originating on CO WDs are often dust-formers and, while C is a major grain component, silicates, polycyclic aromatic hydrocarbons (PAHs), and SiC are often present, occasionally in the same nova (Evans & Gehrz 2012). The evolution of the TNR depends upon the mass and luminosity of the WD, the rate of mass accretion, the composition of the accreted material, and the chemical composition in the reacting layers. Hydrodynamic studies of the accretion process on to the WD preceding the TNR event and the degree to which material from the underlying WD and the envelope is admixed in the ejecta has been studied by many groups for several decades (Politano et al. 1995; Glasner et al. 2012; Kelly et al. 2013; Jos\u00b4 e et al. 2020; Starrfield et al. 2020, 2024). However, the constraints on the theoretical models of nucleosynthesis in the outburst, chemical anomalies related to nucleosynthesis, and the evolution of the progenitor are provided by spectroscopic observations of the ejecta from which detailed elemental abundance patterns can be derived. In this paper we estimate ejecta abundances for V1716 Sco in the coronal line phase of its evolution 132.8 days after outburst (Woodward et al. 2023) derived from photoionization modeling of IR (0.7 to 4.2 \u00b5m) spectra using CLOUDY (Ferland et al. 1998; Chatzikos et al. 2023). These abundance patterns are compared with theoretical simulations of CNe (Starrfield et al. 2020, 2024) with differing core-envelope mixing ratios and their ejecta abundance patterns to understand the characteristics of the underlying WD. Since the coronal phase is fairly prevalent in novae (e.g., the statistics compiled by Benjamin & Dinerstein 1990), the present work may serve as a useful template for comparing results from similar near-IR modeling of CNe that may erupt in the future. 2. V1716 SCO 2.1. General Properties Nova V1716 Sco (PNV J17224490-4137160) was discovered on 2023 April 20.6780 UT by A. Pearce.1 The nova was bright on 2023 April 20.410 UT (MJD 60054.410; Sokolovsky et al. 2023), which we take as our origin of time (to). Its CN status was confirmed by Walter & Pearce (2023), who described it as a lightly-reddened Fe II nova near maximum light. Optical spectroscopy of the earliest phases was obtained by Shore et al. (2023a,b,c) and 1 http://www.cbat.eps.harvard.edu/unconf/followups/J17224490-4137160. html Izzo et al. (2023). The early optical spectra showed ejection velocities \u22431700 km s\u22121, although there were emission components extending to \u00b13000 km s\u22121. The Neil Gehrels Swift Observatory (Gehrels et al. 2004) has observed V1716 Sco regularly since outburst; details will be presented elsewhere. NuSTAR observations of the hard X-ray spectrum of V1716 Sco early in the outburst (Sokolovsky et al. 2023) revealed a heavily absorbed thermal plasma. V1716 Sco joins the increasing inventory of CNe that are \u03b3-ray sources (Cheung et al. 2015, 2018). V1716 Sco is a fast nova (for speed-class definition, see Chomiuk et al. 2021). The AAVSO V-band light curve yields t2 and t3 values (t2 and t3 are the times to decline by 2 and 3 magnitudes respectively from peak brightness) of \u223c5.8 and 11.7 d respectively. 2.2. Distance and Reddening The reddening, EB\u2212V , to V1716 Sco was estimated by Shore et al. (2023b) to be in the range 0.45 < \u223cEB\u2212V < \u223c0.6, consistent with the lower limit (EB\u2212V > \u223c0.5 from diffuse interstellar absorption features) given by Izzo et al. (2023). The methods of van den Bergh & Younger (1987) using the intrinsic colors of CNe give EB\u2212V = 0.66 (color at maximum light) and EB\u2212V = 0.70 (color at time t2). Using the simultaneous solution for AV and distance, D, method described in Kumar et al. (2022), we obtain D = 3.6 \u00b1 0.6 kpc and a somewhat higher value of reddening, EB\u2212V = 1.0. The relative strengths of the OI 0.8446 and 1.1287 \u00b5m lines can be used to estimate the reddening to the nova (Srivastava et al. 2016). Their ratio, as obtained from the spectrum presented here, suggests EB\u2212V \u223c0.57 using a Cardelli et al. (1989) interstellar extinction law. For the present work it seems reasonable to adopt a value of EB\u2212V = 0.65 (the average of all estimates is 0.64 \u00b1 0.18). For a value of EB\u2212V = 0.65, the distance, D, is found to be \u223c2.1 kpc from the extinction versus distance relation derived by Marshall et al. (2006). A 19th magnitude star (Gaia DR3 5959616875349110656) is found to closely match the position of V1716 Sco (the offset between this star and the nova is 0. \u2032\u203242). This star has a parallax of 1.0863 mas and parallax error of 0.3907 mas in the EDR3 database (Gaia Collaboration et al. 2023). A search of the Dark Energy Camera Plane Survey (DECaPS, Saydjari et al. 2023) using a 2. \u2032\u20320 cone search around the position of V1716 Sco with the Astro Data Lab query interface (Nikutta et al. 2020) and the DECaPS DR2 did not return any cataloged points sources. We assume that the Gaia positionally associated source is the progenitor V1716 SCO IR CORONAL ABUNDANCES 3 star of the nova. As recommended for the Gaia data, when the fractional parallax uncertainties are not too large (as applicable in this case) use of the Gaia geometric distance (3.17+2.2 \u22121.6 kpc) is suggested rather than that of the Gaia photogeometric distance, which in this case is 4.97+1.7 \u22121.1 kpc (Bailer-Jones et al. 2021). Thus for the present work we adopt D \u22433 kpc (a value close to the Gaia geometric distance), although there is considerable uncertainty. 3. OBSERVATIONS A 0.7 to 4.2 \u00b5m spectrum of V1716 Sco was obtained on 2023 August 31.24 UT (MJD 60187.24) on the 3.2 m NASA Infrared Telescope Facility (IRTF). Observations were obtained with the medium-resolution facility spectrograph (SpeX, Rayner et al. 2003) in the cross-dispersed short (SXD) and long (LXD short) modes to cover the spectral range of 0.7 4.2 \u00b5m. The observations were made with a 0. \u2032\u20325 slit (R = 1200), at an airmass between 2.10 \u2013 2.24, under photometric conditions and moderate seeing ( < \u223c1. \u2032\u20321 in the K-band). The A0V star HD 148418 was used to correct for telluric absorption and the total on-source integration times for V1716 Sco were 1978s and 556s respectively (the SXD and LXD modes). The SpeX data were reduced and calibrated using Spextool (Cushing et al. 2004) and the tool xtellcor (Vacca et al. 2003) was used for the corrections for telluric absorption. The observed spectrum is presented in Figure 1. The Swift soft X-ray spectrum of 31 August 2023 (MJD 60187.33083 \u00b1 0.00627; obtained within 2 hrs of the IR spectrum) was parametrized by a blackbody and provided an initial estimate for TBB(K). The spectrum is shown in Figure 2 fitted by a BB with kT = 23.6+3.1 \u22123.6 eV, or log T (K) = 5.44. As an initial estimate for the bolometric luminosity Lbol, the BVRI data at maximum from AAVSO were dereddened and fitted by a blackbody to give a temperature of \u223c8400 K equivalent to an outburst luminosity \u2243 1038.45 ergs s\u22121 for a distance of 3 kpc. The latter BB has a radius of 8.9 \u00d7 1012 cm (adopting an expansion velocity of 1000 km s\u22121 and t = 130d). V1716 Sco entered a super-soft x-ray (SSS) phase near day 55 (Page & Kuin 2023). Spectral fits (assuming a simple BB for the SSS source) to all the Swift x-ray spectra suggest only a slight increase in the temperature (\u224330 eV) between day 133 and 180 but nothing significant, as shown in Figure 3. 4. RESULTS 4.1. Photoionization Models 4.1.1. Photoionization Models Cylindrical Geometry The photoionization spectral synthesis code CLOUDY (version C23.01 Chatzikos et al. 2023) was used to model the IR spectroscopic data of V1716 Sco. We assume the surTable 1. V1716 Sco CLOUDY Parameters Cylindrical Day Model +132.8 log TBB(K) 5.74 log L(erg s\u22121) 37.5 log Hden(LD diffuse)(cm\u22123) 6.40 log Hden(HD clump)(cm\u22123) 7.85 log Rin(cm) 15.01 log Rout(cm) 15.3367 log h (cm) 15.35 Covering factor 0.5 Filling factor (diffuse) 0.80 Filling factor (clump) 0.20 Abundancesa) He/H 18.72 \u00d7 10\u22122 C/H 17.41 \u00d7 10\u22124 N/H 167.65 \u00d710\u22124 O/H 93.09 \u00d7 10\u22124 Ne/H 2.18 \u00d7 10\u22124 S/H 98.99 \u00d7 10\u22126 Si/H 71.28 \u00d7 10\u22126 Al/H 16.92 \u00d7 10\u22126 Mg/H 11.94 \u00d7 10\u22125 Ca/H 5.26 \u00d7 10\u22126 P/H 30.84 \u00d7 10\u22126 Fe/H 63.20 \u00d7 10\u22126 Total number of lines 39 Number of free parameters 16 Degrees of freedom 23 Reduced \u03c7 2 2 a)Cloudy23.01 model abundances are optimized assuming the abundances given in Grevesse et al. (2010). NOTE\u2014All other elements have non-depleted (with respect to H) solar abundances. face of the central WD is emitting ionizing blackbody radiation with a temperature TBB(K) and a bolometric luminosity, Lbol (erg s\u22121), irradiating a cylindrical geometry of gas expanding with a velocity of vexp (km s\u22121). The cylindrical model in CLOUDY is basically a truncated spherical model.The dimension of this gas is defined by an inner radius rin (cm), thickness rd (cm), and the height of the cylinder h (cm). CNe often exhibit asymmetric geometries that are highly non-spherical, containing knots and clumps of mate4 WOODWARD ET AL. 0.7 0.8 0.9 1.0 1.1 1.2 1.3 10 13 10 12 10 11 Flux (W m 2 m) a)  H I He I + [S IX] He II O I Fe II ? H I He I [N I] H I [S VIII] H I H I O I [S I] [S XII] [O II] [Fe II] ? O I 1.4 1.6 1.8 2.0 2.2 2.4 10 14 10 13 10 12 Flux (W m 2 m) b)  [Si VII] He I ? [Ca VIII] H I He I + u.i. He I[Al IX] [Si VI] H I H I H I H I + [P VIII] ? H I H I H I u.i. [Si X] He II 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 Wavelength ( m) 10 14 10 13 10 12 Flux (W m 2 m) c)  H I [Si IX] H I [Al VI] [Ca IV] HeII [Mg VII] [Al V] H I Figure 1. The observed spectrum of V1716 Sco on day +132.8, with the prominent lines identified. a) the 0.66 to 1.34 \u00b5m section (SpeX SXD). b) the 1.35 to 2.5 \u00b5m section (SpeX SXD), and c) the 2.80 to 4.20 \u00b5m section. For these latter data, the observed spectral segment (SpeX LXD) was smoothed with a Savtisky-Golay filter of window width = 7, polynomial order = 2, to improve the SNR and each end of the spectral segments were clipped (where the SNR < \u223c3). Unidentified lines are indicated with \u2019u.i.\u2019 The observed spectrum (DbF) for each panel is available as a machine readable table (MRT) in the on-line manuscript. rial (for example V1280 Sco, T Pydixis, or RR Pic, Chesneau et al. 2012; Toraskar et al. 2013; Celed\u00b4 on et al. 2024) motivating use of a cylindrical model. The solar abundances called in the Cloudy modeling are from Grevesse et al. (2010). In the model presented here, we assume a number density law proportional to ninr\u22123, where nin(cm\u22123) is the total hydrogen number density, nin(H0)+nin(H+)+2\u00d7nin(H2)+\u03a3other nin(Hother), (1) the latter term being the summation of other species containing hydrogen nuclei such as H+ 3 , H+ 2 , etc. The observed vexp ranges over 1000 to 1350 km s\u22121. We adopt vexp = 1000 km s\u22121. Hence, both rin (cm) and rd (cm) are set by observation. However, the cylindrical height is a free parameter. The physical parameters and their values for our final \u201cbest-fit\u201d model are listed in Table 1. Later, we consider the observed velocity range as well as an additional model variable. The observed spectrum exhibits highly ionized lines (Si X, Si IX) and neutral lines (H I, O I, He I). The physical processes of forming these lines differ. In the default mode, CLOUDY considers both photoionization and collisional ionization. The collisional ionization rate coefficients are from Voronov (1997) and Dere (2007). In the current model both photoionization and collisional ionization processes are enabled, so strictly it is not a pure photoionization model. However, most of the lines are generated through V1716 SCO IR CORONAL ABUNDANCES 5 0.01 0.1 1 counts s\u22121 keV\u22121 1 0.5 0.5 1 1.5 2 ratio Energy (keV) Figure 2. The Swift x-ray spectrum of V1716 Sco obtained contemporaneously with the near-IR spectrum. The top panel shows a blackbody fit using HEASOFT XSPEC tools (Arnaud 1996) to the soft emission with kT= 23.6+3.1 \u22123.6 eV (or log(T) = 5.44 K). The bottom panel is the ratio of the data to the model fit. 10 2 10 1 100 101 Rate (count s 1) a) 0.0 20.0 40.0 60.0 80.0 BB kT (eV) b) 100 120 140 160 180 200 Days since MJD 60054.41 0.0 0.5 1.0 1.5 2.0 NH (1022 cm 2) c) Figure 3. Synoptic Swift observations of V1716 Sco post outburst and spectral fits. a) The light curve. b) The derived kT (eV) from model fits assuming a simple blackbody for the SSS for the soft x-ray spectra (red points with associated asymmetric error). Only a modest variance in the overall temperature of the x-ray source from day 133 through day 190 is evident. c) The derived hydrogen column density (blue dots with associated asymmetric errors). The data for each panel are available as a machine readable table (MRT) in the on-line manuscript. photoionization and recombination. CLOUDY has options to use these processes separately. However, for V1716 Sco, the combined photoionization and collisional model works better (as compared to the observations) than a solely collisional or solely photoionization model. We assume a two component model, consisting of high (\u201cclump\u201d) and low densities (\u201cdiffuse\u201d). The highly ionized lines arise from the low density component (A), whereas the neutral lines arise from the high density component (B). While the density and the filling factors for these two com6 WOODWARD ET AL. ponents are different, the other modeling parameters are the same. Our final model predicts an average hydrogen density at the inner radius, rin for components A and B to be log Hden (cm\u22123) = 6.4 and 7.85, respectively. Component A and component B contain 12% and 88% of the volume of the ejecta, respectively. In component B, a density higher than log Hden = 7.85 reduces the forbidden line fluxes due to increased collisional de-excitations. We find that a blackbody of temperature 105.74 K with bolometric luminosity 1037.5 erg s\u22121 is required to reproduce the observed line intensities on day 133. This high blackbody temperature is necessary to reproduce highly ionized line fluxes, such as for Si IX. On the other hand, a luminosity of 1037.5 erg s\u22121 makes the forbidden lines much weaker and the H I lines much stronger than is observed. The physical parameters and their values for the cylindrical model best-fit are listed in Table 1. We vary only the elemental abundances of the observed lines (He, O, N, Mg, P, Ca, Al, S, Si). Most of the predicted line intensities match with their observed values within the observed uncertainties (see Table 2). 4.1.2. Photoionization Models Spherical Geometry As a check, we consider a spherical geometry of the ejecta. In Table 3, we present our predictions for the spherical model keeping all the input parameters the same as the cylindrical model. Our model predictions with a cylindrical geometry match better with the observations despite the cylindrical model being a very simple truncated spherical model (see Fig. 4). Hence, we consider the cylindrical model as our best fit model. 4.1.3. Photoionization Models Ejecta Velocity Observation reveals that vexp ranges from 1000 1350 km s\u22121, i.e., close to half the FWHM of the hydrogen Paschen-\u03b2 line of 2700 km s\u22121. Generally the vexp is typically half the FWHM for any expanding spherical shell of gas (Robinson et al. 1982). Hence, for the cylindrical model, we assume the low density component expanding at 1350 km s\u22121 which is greater than the expansion velocity of the dense component. The results are listed in Table 4. This model increases the [Si X] line flux by 0.05 dex. Considering all the three cases mentioned above, (see Fig. 4), a cylindrical model with low density region expanding with a higher velocity than the high density region seems to be the best fit model. 4.1.4. Photoionization Models Goodness of Fit The \u03c72, the goodness of fit of a model to the observed spectrum, is determined by the following relation, \u03c72 = n X i=1 (Mi \u2212Oi)2 \u03c32 i (2) [O II] 0.7320/30 OI 0.8446 HI 0.9229 HI 0.9545 [S VIII] 0.9914 HI 1.0049 N I 1.0404 HeI 1.0830 HI 1.0938 OI 1.1287 HeII 1.1626 HeI + [S IX] 1.252 HI 1.2818 PVII 1.3745 [Si X] 1.4300 HI 1.6109 HI 1.6407 HI 1.6806 PVIII 1.7393 HI 1.7362 HI 1.8174 HI 1.8751 HI 1.9445 [Si VI] 1.9624 [Al IX] 2.0444 HeI 2.0581 HI 2.1655 HeII 2.1884 [Ca VIII]  2.3211 [Si VII] 2.4801 [Al V] 2.9045 [Mg VIII] 3.0276 [Ca IV] 3.2061 HeII 3.0908 AlVIII 3.6972 HI 3.7395 [Si IX] 3.9282 HI 4.0511 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0 9.5 Log Line Flux (erg s 1 cm 2) a) Cloudy Cylindrical Model Observed Dereddend Line Flux [O II]  0.7320/30 OI 0.8446 HI 0.9229 HI 0.9545 [S VIII] 0.9914 HI 1.0049 [N I] 1.0404 HeI 1.0830 HI 1.0938 OI 1.1287 HeII 1.1626 HeI + [S IX] 1.252 HI 1.2818 PVII 1.3745 [Si X] 1.4300 HI 1.6109 HI 1.6407 HI 1.6806 PVIII 1.7393 HI 1.7362 HI 1.8174 HI 1.8751 HI 1.9445 [Si VI] 1.9624 [Al IX] 2.0444 HeI 2.0581 HI 2.1655 HeII 2.1884 [Ca VIII] 2.3211 [Si VII] 2.4801 [Al V] 2.9045 [Mg VIII] 3.0276 [Ca IV] 3.2061 HeII 3.0908 [Al VI] 3.6593 AlVIII 3.6972 HI 3.7395 [Si IX] 3.9282 HI 4.0511 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0 9.5 Log Line Flux (erg s 1 cm 2) b) Cloudy Spherical Model Observed Dereddend Line Flux [O II] 0.7320/30 OI 0.8446 HI 0.9229 HI 0.9545 [S VIII] 0.9914 HI 1.0049 [N I] 1.0404 HeI 1.0830 HI 1.0938 OI 1.1287 HeII 1.1626 HeI + [S IX]  1.252 HI 1.2818 PVII 1.3745 [Si X] 1.4300 HI 1.6109 HI 1.6407 HI 1.6806 PVIII 1.7393 HI 1.7362 HI 1.8174 HI 1.8751 HI 1.9445 [Si VI] 1.9624 [Al IX] 2.0444 HeI 2.0581 HI 2.1655 HeII 2.1884 [Ca VIII] 2.3211 [Si VII] 2.4801 [Al V] 2.9045 [Mg VIII] 3.0276 [Ca IV] 3.2061 HeII 3.0908 [Al VI] 3.6593 AlVIII 3.6972 HI 3.7395 [Si IX] 3.9282 HI 4.0511 13.5 13.0 12.5 12.0 11.5 11.0 10.5 10.0 9.5 Log Line Flux (erg s 1 cm 2) c) Cloudy Cylindrical Model vexp(LD) >  vexp(HD) Observed Dereddend Line Flux Figure 4. Observed dereddened line fluxes (red filled circles) versus CLOUDY line fluxes (blue filled circles). a) From the best-fit cylindrical model (Table 2). b) From a spherical model (Table 3). c) From the best-fit cylindrical model (Table 4) where the LD component is expanding with a velocity greater than the HD component. where n is the number of emission lines used in the model, Mi and Oi are the modeled and observed line flux ratios (line fluxes were normalized with respect to the Paschen-\u03b2 line), and \u03c3i is the error in the observed line flux ratios. The reduced \u03c72 (reported in Table 1) is given by \u03c72 red = \u03c72/\u03bd, where \u03bd is the number of degrees of freedom, given by the difference between the number of observed emission lines (n) and the number of free parameters (np), where \u03bd = n \u2212np. For acceptable fitting, the value of \u03c72 \u223c\u03bd and \u03c72 red should be low, typically between 1 and 2. The value of \u03c3 genV1716 SCO IR CORONAL ABUNDANCES 7 Table 2. V1716 Sco Observed and CLOUDY Line Luminosities for the Cylindrical Model log flux\u2020 log flux\u2020 log total flux Dereddend Line (LD) (HD) (HD + LD) Observed Flux (\u00b5m) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) [O II] 0.7320/30 -20.13 -11.10 -11.10 -11.16 OI 0.8446 <-20.00 -11.62 -11.62 -11.77 HI 0.9229 -13.96 -11.86 -11.86 -11.69 HI 0.9545 -13.80 -11.72 -11.71 -11.75 [S VIII]] 0.9914 -11.91 -11.47 -11.33 -11.50 HI 1.0049 -13.62 -11.54 -11.54 -11.24 [N I]1.0404 <-20.00 -11.50 -11.50 -11.54 HeI 1.0830 -14.99 -10.14 -10.14 -10.30 HI 1.0938 -13.42 -11.33 -11.33 -11.27 OI 1.1287 <-20.00 -11.75 -11.75 -11.92 HeII 1.1626 -13.39 -12.09 -12.07 -12.02 HeI + [S IX] 1.252 -11.93 -12.36 -11.79 -11.74 HI 1.2818 -13.13 -11.07 -11.07 -11.23 PVII 1.3745 -13.43 -11.50 -11.50 -11.67 [Si X] 1.4300 -11.99 -16.21 -11.97 -11.75 HI 1.6109 -14.81 -12.66 -12.66 -12.71 HI 1.6407 -14.70 -12.57 -12.57 -12.60 HI 1.6806 -14.58 -12.47 -12.47 -12.28 PVIII 1.7393 -12.47 -12.35 -12.10 -12.04 HI 1.7362 -14.47 -12.36 -12.36 -12.04 HI 1.8174 -14.33 -12.23 -12.23 -11.99 HI 1.8751 -12.86 -10.76 -10.76 -10.81 HI 1.9445 -14.17 -12.08 -12.08 -12.10 [Si VI] 1.9624 -14.50 -10.98 -10.98 -11.34 [Al IX] 2.0444 -11.97 -14.48 -11.97 -12.07 HeI 2.0581 -19.04 -12.17 -12.17 -12.07 HI 2.1655 -13.99 -11.91 -11.91 -11.97 HeII 2.1884 -14.26 -12.97 -12.95 -12.73 [Ca VIII] 2.3211 -12.71 -14.47 -12.70 -12.38 [Si VII] 2.4801 -12.59 -11.27 -11.25 -11.19 [Al V] 2.9045 -17.24 -11.84 -11.84 -11.95 [Mg VIII] 3.0276 -11.16 -13.02 -11.15 -11.11 [Ca IV] 3.2061 -18.70 -12.41 -12.41 -12.31 HeII 3.0908 -13.66 -12.34 -12.32 -12.07 [Al VI] 3.6593 -14.28 -12.02 -12.02 -11.88 AlVIII 3.6972 -12.50 -13.72 -12.47 -12.49 HI 3.7395 -14.46 -12.37 -12.37, -12.34 [Si IX] 3.9282 -11.48 -14.96 -11.48 -11.67 HI 4.0511 -13.55 -11.50 -11.49 -11.60 NOTE\u2014\u2020 LD/HD = low/high density. 8 WOODWARD ET AL. Table 3. V1716 Sco Observed and CLOUDY Line Luminosities for the Spherical Model\u2021 log flux\u2020 log flux\u2020 log total flux Dereddend Line (LD) (HD) (HD + LD) Observed Flux (\u00b5m) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) [O II] 0.7320/30 -20.60 -11.27 -11.27 -11.16 OI 0.8446 <-20.00 -11.94 -11.94 -11.77 HI 0.9229 -14.52 -11.71 -11.71 -11.69 HI 0.9545 -14.36 -11.56 -11.56 -11.75 [S VIII] 0.9914 -12.48 -11.46 -11.42 -11.50 HI 1.0049 -14.18 -11.39 -11.39 -11.24 [N I] 1.0404 <-20.00 -11.43 -11.43 -11.54 HeI 1.0830 -15.37 -10.03 -10.03 -10.30 HI 1.0938 -13.97 -11.17 -11.17 -11.27 OI 1.1287 <-20.00 -11.07 -11.07 -11.92 HeII 1.1626 -13.95 -12.09 -12.07 -12.02 HeI + [S IX] 1.252 -12.45 -12.25 -12.04 -11.74 HI 1.2818 -13.65 -10.91 -10.91 -11.23 PVII 1.3745 -14.02 -11.50 -11.50 -11.67 [Si X] 1.4300 -12.40 -16.20 -12.40 -11.75 HI 1.6109 -15.36 -12.51 -12.51 -12.71 HI 1.6407 -15.25 -12.42 -12.42 -12.60 HI 1.6806 -15.14 -12.32 -12.32 -12.28 PVIII 1.7393 -13.04 -12.35 -12.27 -12.04 HI 1.7362 -15.02 -12.21 -12.21 -12.04 HI 1.8174 -14.88 -12.08 -12.08 -11.99 HI 1.8751 -13.38 -10.59 -10.59 -10.81 HI 1.9445 -14.72 -11.93 -11.93 -12.10 [Si VI] 1.9624 -15.09 -10.98 -10.98 -11.34 [Al IX] 2.0444 -12.50 -14.48 -12.50 -12.07 HeI 2.0581 -19.50 -12.07 -12.07 -12.07 HI 2.1655 -14.54 -11.76 -11.75 -11.97 HeII 2.1884 -14.82 -12.97 -12.96 -12.73 [Ca VIII] 2.3211 -13.34 -14.47 -13.31 -12.38 [Si VII] 2.4801 -13.16 -11.26 -11.26 -11.19 [Al V] 2.9045 -17.84 -11.82 -11.82 -11.95 [Mg VIII] 3.0276 -11.72 -13.02 -11.70 -11.11 [Ca IV] 3.2061 -19.36 -12.40 -12.40 -12.31 HeII 3.0908 -14.22 -12.34 -12.33 -12.07 [Al VI] 3.6593 -14.88 -12.02 -12.02 -11.88 AlVIII 3.6972 -13.06 -13.72 -12.97 -12.49 HI 3.7395 -15.00 -12.21 -12.21 -12.34 [Si IX] 3.9282 -11.98 -14.95 -11.98 -11.67 HI 4.0511 -14.08 -11.33 -11.33 -11.60 NOTE\u2014 \u2021 All Cloudy input parameters are identical to the cylindrical model. \u2020 LD/HD = low/high density. V1716 SCO IR CORONAL ABUNDANCES 9 Table 4. V1716 Sco Observed and CLOUDY Line Luminosities for the Cylindrical Model where LD is expanding with a higher velocity than the HD log flux\u2020 log flux\u2020 log total flux Dereddend Line (LD) (HD) (HD + LD) Observed Flux (\u00b5m) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) (erg s\u22121 cm\u22122) [O II] 0.7320/30 -20.13 -11.10 -11.10 -11.16 OI 0.8446 <-20.00 -11.62 -11.62 -11.77 HI 0.9229 -13.95 -11.86 -11.86 -11.69 HI 0.9545 -13.80 -11.72 -11.71 -11.75 [S VIII] 0.9914 -11.90 -11.47 -11.33 -11.50 HI 1.0049 -13.62 -11.54 -11.54 -11.24 [N I] 1.0404 <-20.00 -11.50 -11.50 -11.54 HeI 1.0830 -14.99 -10.14 -10.14 -10.30 HI 1.0938 -13.40 -11.33 -11.33 -11.27 OI 1.1287 <-20.00 -11.75 -11.75 -11.92 HeII 1.1626 -13.38 -12.09 -12.07 -12.02 HeI + [S IX] 1.252 -11.92 -12.36 -11.78 -11.74 HI 1.2818 -13.12 -11.07 -11.07 -11.23 PVII 1.3745 -13.42 -11.50 -11.50 -11.67 [Si X] 1.4300 -11.94 -16.21 -11.94 -11.75 HI 1.6109 -14.80 -12.66 -12.66 -12.71 HI 1.6407 -14.69 -12.57 -12.57 -12.60 HI 1.6806 -14.57 -12.47 -12.47 -12.28 PVIII 1.7393 -12.46 -12.35 -12.10 -12.04 HI 1.7362 -14.46 -12.36 -12.36 -12.04 HI 1.8174 -14.32 -12.23 -12.23 -11.99 HI 1.8751 -12.85 -10.76 -10.76 -10.81 HI 1.9445 -14.16 -12.08 -12.08 -12.10 [Si VI] 1.9624 -14.50 -10.98 -10.98 -11.34 [Al IX] 2.0444 -11.96 -14.48 -11.96 -12.07 HeI 2.0581 -19.04 -12.17 -12.17 -12.07 HI 2.1655 -13.98 -11.91 -11.91 -11.97 HeII 2.1884 -14.25 -12.97 -12.95 -12.73 [Ca VIII] 2.3211 -12.71 -14.47 -12.70 -12.38 [Si VII] 2.4801 -12.59 -11.27 -11.25 -11.19 [Al V] 2.9045 -17.24 -11.84 -11.84 -11.95 [Mg VIII] 3.0276 -11.15 -13.02 -11.14 -11.11 [Ca IV] 3.2061 -18.70 -12.41 -12.41 -12.31 HeII 3.0908 -13.65 -12.34 -12.32 -12.07 [Al VI] 3.6593 -14.28 -12.02 -12.02 -11.88 AlVIII 3.6972 -12.49 -13.72 -12.47 -12.49 HI 3.7395 -14.45 -12.37 -12.37 -12.34 [Si IX] 3.9282 -11.46 -14.96 -11.46 -11.67 HI 4.0511 -13.54 -11.50 -11.49 -11.60 NOTE\u2014 \u2020 LD/HD = low/high density. 10 WOODWARD ET AL. erally lies in the range of 10% to 50% (e.g., Vanlandingham et al. 2005; Helton et al. 2010; Habtie et al. 2024) depending on several factors including (a) uncertainties in the dereddening value which is wavelength dependent (it is as large as 20% near 0.7 \u00b5m, for an error of 0.1 in the EB\u2212V value), (b) the actual measurement of the line fluxes, (c) the process of removing the H lines from the standard A0V star spectrum before ratioing the nova spectrum (the H lines are numerous, consisting of lines from the Paschen, Brackett, Pfund and Humphreys series), and (d) blending of lines which is a major source of uncertainty in many cases. Given these factors, we consider \u03c3 = 35% for the present study (25% for each line measurement and hence 35% for each line ratio relative to Paschen-\u03b2 1.2818 \u00b5m; the error being added in quadrature while ratioing). In our analysis the total number of lines is 39, the number of free parameters = 16 and hence the degrees of freedom are 23. We thus get a \u03c72 = 59.8 and a reduced \u03c72 red = 2.6. A major part of the \u03c72 value comes from 2 lines, the [O II] 0.7320, 30 \u00b5m line (\u03c72 = 7.7) and from the [Si VI] 1.96 \u00b5m line (\u03c72 = 12.8). If these two lines are omitted, \u03c72 red \u22431.87. This is acceptable especially since the assumption of a cylindrical geometry is a significant simplification (e.g., Pandey et al. 2022; Habtie et al. 2024). He N O Mg Al Si S Ca P Fe C Ne Element 10 1 100 101 102 103 Xi (Elemental Abundance) / Xi (Solar Abundance) V1716 Sco Cloudy23.01 SS CO2575 1.0 Solar Mass Figure 5. The observed abundances (red triangles) derived from the Cloudy photoionization model (assuming a cylindrical geometry) versus model abundance values obtained from tabulated mass fractions (blue squares, Starrfield et al. 2020) for a 1.0 M\u2299CO nova with 25-75% mixing (see Section 4.2 for further details). Solar abundance values are taken from Grevesse et al. (2010). The dashed line across the plot represents solar abundances. The blue square for Fe is set to the solar abundance value as the temperatures reached in the model TNRs are insufficient to produce Fe. The TNR event itself removes the original abundance heritage of the material accreted onto the WD surface by explosive nucleosynthesis reactions (Starrfield et al. 2020, 2024). 4.2. Abundances Estimates and WD Ejecta Mixing A comparison of the observed line intensities with the coadded CLOUDY line intensities (the fluxes of high and low density components are co-added) is presented in Figure 4. Considering that a variety of lines are seen (recombination lines, lines from neutral species, lines from highly ionized atoms, Ly\u03b2 fluoresced lines), a reasonably good reproduction of line strengths is seen in Figure 4. H is depleted from nuclear burning in the TNR. We find (Figure 5) that the observationally derived abundances of He, Ne, C, O, Fe, Al, Si, S and Ca are mildly to moderately above solar. The abundances (by mass) with respect to the Sun (Grevesse et al. 2010) are He = 2.20, C = 6.47, O = 18.99, Ne = 2.56, Mg = 3.00, Al = 6.00, Si = 2.20, S = 7.50, Ca = 2.42, Fe = 2.00, N = 248.00 and P = 120.0. Notably, phosphorus and nitrogen are highly overabundant. However, this is consistent with the predictions of Starrfield et al. (2020, 2024) wherein P is predicted to be 100 or more times overabundant (compared to solar) for massive ONe or CO WDs. For example, for a 1.25 M\u2299 CO WD with 25-75% mixing the value of P is \u223c100. The P overabundance may be suggesting that V1716 Sco harbors a massive WD ( > \u223c1.0 M\u2299) which is consistent with its short t2, (see Section 2.1). We have compared the derived abundances with those expected in the nucleosynthesis models of Starrfield et al. (2020) as illustrated in Figure 5. This figure compares the observed CLOUDY deduced yields in V1716 Sco with one of the Starrfield et al. (2020) models of an 1.0 M\u2299WD with a CO core with 25-75% mixing. A mixing ratio of 25-75% means that the material that undergoes a TNR has a composition of 25% of the outer layers of the underlying WD mixed with 75% of the accreted envelope during the to thermonuclear runaway. The agreement is reasonable for many of the elements. It is not known whether V1716 Sco contains a WD of the CO or ONe type. The mass of the WD is also not known. However the Fe II classification of the nova (Walter & Pearce 2023) strongly suggests a CO type. Figure 6 shows a comparison of different models of Starrfield et al. (2020, 2024) for both CO and ONe novae with different WD masses and mixing fractions. For each of the CO and ONe classes, there are six Starrfield models shown with WD masses of 0.6, 0.8, 1.0, 1.15, 1.25 and 1.35 M\u2299respectively. For each WD mass, two mixing fractions are considered that of 25-75% and 5050%. Thus there are a total of twenty-four Starrfield et al. (2020, 2024) models. Kelly et al. (2013) investigated whether or not observed ONe nova abundances can be used to constrain the degree of mixing that occurs between the outer layers of the underlying WD and the accreted envelope prior to TNR. Any abundance used for this purpose, was referred to as a mixing meter. Comparison of mixing meters with observations allowed for an estimate of the mixing fractions in individual V1716 SCO IR CORONAL ABUNDANCES 11 novae. They found a fraction of 25% or smaller for the mixing between WD matter and the accreted envelope in almost all cases (ONe models). Therefore, Kelly et al. (2013) concluded that the observations support a mixing fraction that is much smaller than 50%, which has usually been used in the literature. In Figure 6, the meter used is the quantity S defined as S = 1 N n X i=1 \u0010xobs(i) x\u2299 \u2212xmodel(i) x\u2299 \u00112 (3) where the summation is over N (= 11), the number of elements with derived CLOUDY abundances whose mass fractions are compared to those derived for the ejecta for various WD mass in the TNR models of Starrfield et al. (2020, 2024). On the X-axis, each tick label (e.g., CO 2575) gives the the type of the WD (CO or ONe) and the mixing fraction (e.g., 25-75%). Comparing the CO 5050 and CO 2575 values in Figure 6, it is clear that the latter set has much smaller scatter and smaller S values strongly suggesting that a 25-75% mixing fraction is certainly favored over a 50-50% mixing for V1716 Sco. Further, inter-comparison between the SS ONe and CO models, shows that the observed abundances in V1716 Sco match the CO novae better. A similar conclusion is reached comparing to models by Jos\u00b4 e et al. (2020). This suggests that V1716 Sco is a CO nova, an inference that is consistent with the CO classification proposed in Section 2.1, based on the Fe II spectral classification. Absence of neon lines in the spectra at day 133 also suggests that the binary contains a CO WD, although late-time observations when the source enters a nebular phase combined with detailed abundance modeling may be necessary to confirm the latter assertion (e.g., see the cautionary note in Schwarz et al. 2007) as [Ne V] 3550/3426 \u02da A was detected by Swift near the onset of the SSS phase (Page & Kuin 2023). As a check for the sensitivity of the results of Figure 6 to errors in the observed flux, we ran an additional two sets of computations with the abundances of all the elements under consideration uniformly increased (or decreased) by \u00b1 20% with respect to H. No significant changes are seen to the results presented in Figure 6. 4.3. Ejecta Mass The mass (Mshell) in a cylindrical volume of height h can be calculated in units of M\u2299from the parameters presented in Table 1 by the expression: Mshell = \u03c0 mp (r2 out \u2212r2 in) h (fHDnHD + fLDnLD) X (1 + Ai) (4) CO_5050 CO_2575 ONe_5050 ONe_2575 10 2 10 1 S CO_5050 CO_2575 ONe_5050 ONe_2575 Figure 6. Comparison of TNR mixing values to derived abundances in V1716 Sco. Each tick label on the X-axis (e.g., CO 2575) gives the model values taken from Starrfield et al. (2020, 2024), the type of the WD (CO or ONe) and the mixing fraction (e.g., 25-75%). The multiple points along the Y axis for each tick label correspond to the S values for the different 6 WD masses (0.6, 0.8, 1.0, 1.15, 1.25, and 1.35 M\u2299) considered in the latter references. S is essentially a meter to broadly measure how well the observed abundances in V1716 Sco match with nucleosynthesis models (see Section 4.2). A small value of S implies a good agreement. where fHD, nHD, fLD, nLD are the filling factors and H densities for the high (\u201cclumps\u201d) and low density (\u201cdiffuse\u201d) components (abbreviated as HD and LD respectively) given in Table 1, mp is the proton mass, and the summation is over the fractional mass of the elements in the shell with respect to hydrogen (using the fraction-by-numbers data in Table 1; other elements not listed in Table 1 are assumed to have solar values). We obtain a mass of \u22434.19 \u00d7 10\u22124 M\u2299, (adopting average values of nHD and nLD assuming n(r) = n(rin) \u00d7 r\u22123 where \u223c88% is in the HD component and \u223c12% is in the LD component. This ejected mass estimate is greater than those predicted from TNR models. However, this is a well known tension that has plagued studies of the nova phenomena for decades (e.g., Starrfield 1999; Woodward & Starrfield 2011). The underlying cause for this discrepancy is not understood. 5. DISCUSSION 5.1. Interpretation of Line Profiles and CLOUDY There is a clear difference between the shape of the line profiles of the H and He lines, both of which arise from the dense component, and the coronal lines (with ionization potentials of the lower ionization state > \u223c225 ev), which mostly arise from the low density component (Table 2). This is illustrated in Figure 7. H and He lines are broad with a castellated peak emission profile, whereas the infrared coronal lines exhibit distinct double-peaked structures with a deep dip between the 12 WOODWARD ET AL. peaks (a notched saddle profile) centered near \u22430 km s\u22121. The lines showing this structure are listed in Table 5 along with the peak-to-peak separation. The highest velocity, common H I recombination line components (Figure 7d) at \u00b1950 km s\u22121 are coincident with the double peak profiles seen in neutral oxygen, while the coronal line double peaks are at higher velocities \u00b11100 km s\u22121 . Wings of the coronal lines exhibit even higher velocity substructures in their profiles. The FWHM of the [Mg VIII] profile (Figure 7c) is \u22433400 km s\u22121. The velocity structures and FWHM suggest that the lines arise from different regions within the ejecta. This is expected because the forbidden coronal lines will be collisionally de-excited in a region that is denser than the critical density of the line (Woodward et al. 2021; Kumar et al. 2022). What is puzzling is that the O I 0.8446 and 1.1287 \u00b5m line profiles (excitation potential 12.03 ev, Keenan & Hynek 1950; Bhatia & Kastner 1995) also show a similar profile (albeit somewhat narrower in peak-to-peak separation) as the coronal lines. Modeling indicates (Table 2) oxygen lines also arise within denser regions of the ejecta. A significant part of the strength of both the 0.8446 and 1.1287 \u00b5m lines is from Lyman-\u03b2 fluorescence. So it is consistent that the sites of O I and H emission are co-spatial (Figure 7a) ensuring an adequate input of Ly-\u03b2 photons from the recombination cascade process in hydrogen. If the H emitting region is optically thick, Ly-\u03b2 photons may even get trapped. Thus the necessary sources of Ly-\u03b2 photons are available for fluorescing the O I lines. However, the O I lines show a considerably smaller expansion velocity (FWHM \u22431350 km s\u22121) than the other coronal lines (FWHM > \u223c3000 km s\u22121) strongly suggesting that they originate from different regions despite sharing the same doublepeaked profile shape. Likely the V1716 Sco ejecta nebula is not spherically symmetric, but bipolar in morphology. Bipolar morphologies are directly detected in several novae, such as V1280 Sco (Chesneau et al. 2012; Pandey et al. 2022), RS Oph (Bode et al. 2007), V959 Mon (Healy et al. 2017, and references therein) and V445 Pup (Woudt et al. 2009; Nyamai et al. 2021), by using high spatial resolution imaging techniques and interferometry; hence this geometry is common (and why Cloudy models in Section 4.1 explore cylindrical geometries). In V1716 Sco, denser regions in the asymmetrical ejecta could be the site of the O I 0.8446/1.1287 \u00b5m lines and the O I double-peaked profiles could arise from the receding and approaching parts of these lobes. The strong shock created by the ejecta colliding with dense globules, or denser toroidal material within the ejecta could likely have given rise to the \u03b3-rays seen during the outburst. The geometric scenario for the \u03b3-ray generation proposed here would then be similar to that proposed for the \u03b3-ray nova V959 Mon (Chomiuk et al. 2014). In comparison to the O I lines, the coronal lines with a higher velocity (Table 5), could originate from the bipolar lobes which are expected to be more diffuse and also to have a higher velocity compared to the material in a constricting denser torus. Some of the coronal lines with high critical densities in the range of 108 to 109 cm\u22123, like the [Si VI] 1.96 and [Si VII] 2.48 \u00b5m lines for gas temperatures in excess of 105 K, (Evans et al. 2023) could come from both the torus and bipolar lobes. Hence their line profiles are expected to be as evident in Figure 7. The [N I] 0.5755 \u00b5m and 1.04 \u00b5m lines, together with the [O I] 0.6300, 0.6364 \u00b5m doublet, are among the first forbidden lines to appear in the spectra of novae (particularly the Fe II novae) and they remain present even after high ionization lines appear in the spectra (Williams et al. 1994; Aydi et al. 2024). The [N I] 1.04 \u00b5m line is seen here and inspection of optical spectra from the ARAS database2 shows that [O I] 0.6300, 0.6364 \u00b5m lines were present before and during the current observations on day 133. Based on several characteristics of the [O I] emission, Williams et al. (1994) has convincingly argued that dense globules must exist in the ejecta and that the [O I] emission comes from within these globules (these globules are likely sites for dust formation too). Just like the [O I] lines, it would appear reasonable to expect that neutral [N I] 1.04 \u00b5m emission also originates from material in the dense globules, where nitrogen atoms can remain shielded and neutral. This is supported by the data in Table 2 which show that [N I] emission arises from the dense component and is absent in the diffuse component. However, the line profiles (Figure 7) alternatively could be interpreted as being consistent with a single ejecta component (non-spherical, axisymmetric, and inhomogeneous) with just a density gradient imposed by the expansion velocity law. In this picture the higher velocity regions would inevitably be the ones with the lowest density, explaining the broader width and larger peak separation of the IR coronal lines. Conversely in the lower (inner, for an explosive expansion law) velocity regions, recombination occurs, and Ly-\u03b2 can be sufficiently optically thick to pump the observed O I transition. 5.2. Observed coronal lines not replicated by CLOUDY There are two emission lines at \u223c1.55 and \u223c2.09 \u00b5m which are often seen during the coronal stage in many novae, for example V1974 Cyg (Wagner & Depoy 1996), RS Oph (Banerjee et al. 2009), V1674 Her (Woodward et al. 2021) and V6558 Sgr (Gehrz et al. 2018), whose identification has remained uncertain. These lines are thought to be coronal in nature because they arise during the coronal phase and their broader profile shapes (e.g., FWHM and peak-to-peak sepa2 http://www.astrosurf.com/aras/Aras DataBase/Novae.htm V1716 SCO IR CORONAL ABUNDANCES 13 rations) often replicate the coronal line profiles shapes (see Gehrz et al. 2018, for a discussion on the 2.09 \u00b5m profile shape) rather than the H or He line profiles shapes and substructures (see Figure 7 for example). The line at \u223c1.55 \u00b5m (labeled \u2018u.i.\u2019, see Figure 1) has been thought to be either [Si IX] 1.55995 \u00b5m or [Cr XI] 1.5518 \u00b5m (Wagner & Depoy 1996). However, our CLOUDY calculations underproduce the [Si IX] 1.55995 \u00b5m line by a factor of 23,000, while the observed line center is at 1.5534 \u00b5m, displaced by 0.0065 \u00b5m from the expected position. It is unlikely that this line is [Si IX]. Similarly the observed fluxes of the [Cr XI] 1.5518 and [Mn XIV] 2.09 \u00b5m lines in V1716 Sco cannot be matched by CLOUDY even if both these elements are 1000 times overabundant compared to their solar values. It is thus likely that the [Cr XI] and [Mn XIV] assignments to these lines are incorrect. In our CLOUDY models, the strongest lines between 1.5528 1.5601 \u00b5m are C IV in the low density component, and blends of He I + H I + C IV in the high density component. 5.3. Do CNe Produce Helium Hydride (HeH+) ? The spectrum of V1716 Sco consists mainly of atomic and ionic lines. However our final CLOUDY model predicts an observable amount of the helium hydride ion, HeH+, in component B (denser component) at a significant column density of 1012.959 cm\u22122. The dominant formation channel for HeH+ is He+ + H \u2192HeH+ + h\u03bd. Uncertainties in chemical reaction rate coefficients influence the predicted abundances/column densities of the species involved. We adopted the rate coefficient for this reaction from Zygelman & Dalgarno (1990). There can be 30% uncertainty in the predicted column density due to the uncertainties in the chemical rate coefficients (Zygelman & Dalgarno 1990). After the Big Bang, in the early Universe\u2019s metal-free and low-density environment, the first molecule to form was HeH+, following radiative association of He atoms with protons. HeH+ has recently been discovered toward the planetary nebula NCG 7027 via the rotational transition at 149.1 \u00b5m (G\u00a8 usten et al. 2019). HeH+ in NGC 7027 has a column density that is similar to that found here for V1716 Sco. The conditions in planetary nebulae are known to be suitable for the production of potentially detectable HeH+ column densities: the hard radiation field from the central hot WD creates overlapping Str\u00a8 omgren spheres (G\u00a8 usten et al. 2019) where HeH+ is predicted to form. Figure 8 shows that a similar situation exists in V1716 Sco (and may possibly exist in other novae) with a similar overlapping of He+ and H zones (the CLOUDY model is a timeindependent model, hence these are overlapping Str\u00a8 omgren spheres) having substantial number densities of HeH+. In the near-IR, HeH+ has a few ro-vibrational features, e.g., the \u03bd = 1 \u22120 P(1) 3.51629 \u00b5m line, the P(2) 3.60776 \u00b5m Table 5. Lines with double peaked profiles Line Peak-to-Peak Line Peak-to-Peak separation separation (\u00b5m) (km s\u22121) (\u00b5m) (km s\u22121) O I 0.8446 1705 [Si X] 1.4300 2350 [S VIII] 0.9914 1970 \u2018u.i.\u2019 1.5599 2120 O I 1.1287 1807 [Mg VIII] 3.0276 2070 [S IX] 1.2523 2275 [Si IX] 3.9282 2288 line, and the \u03bd = 1 \u22120 R(0) ro-vibrational line at 3.364 \u00b5m. The first two of these lines have been detected in NGC 7027 (Neufeld et al. 2020). The line fluxes of these three lines, based on the CLOUDY number densities, need to be calculated theoretically (which is outside the scope of this work) to know whether they should be detectable. However, close examination of our spectrum of V1716 Sco reveals no significant emission at the wavelength positions of these lines, though the atmospheric transmission in the spectral region covered by these lines is poor. The study of other CNe with the high sensitivity achievable with the JWST NIRspec may unambiguously detect the presence of this important hydride, and even its evolution in real time or provide more definitive observational evidence that rebuts the conjecture. 6. CONCLUSION A moderate resolution near-IR spectrum of V1716 Sco during the coronal line phase of evolution obtained 132.8 days post-outburst was modeled by using the photoionization code CLOUDY. Abundances were estimated for H, He, N, O, Si, Al, Mg, S, Ca and P. Except for H, the analyzed elements are over-abundant compared to solar values. The abundances (by mass) with respect to the Sun are He = 2.20, C = 6.47, O = 18.99, Ne = 2.56, Mg = 3.00, Al = 6.00, Si = 2.20, S = 7.50, Ca = 2.42, Fe = 2.00, N = 248.00 and P = 120.0. It was necessary to consider the ejecta to be composed of two components. One, a dense component from which the bulk of the H, He, OI and N emission arises and second, a less dense component from which most of the coronal lines arise. Some of the coronal lines are found to arise from both components. A cylindrical (non-spherical) geometry for the ejecta in photoionization modeling best reproduces the observed IR line fluxes. The mass of the ejecta, including neutral and ionized gas, is \u22434.19 \u00d7 10\u22124 M\u2299. 14 WOODWARD ET AL. The Ly-\u03b2 fluoresced O I 0.8446 and 1.1287 \u00b5m lines exhibit a prominent double-peaked structure; a profile shape that the O I lines share with several coronal lines. Finally, the derived abundance yields were compared to various simulations of the TNR event to assess and constrain the level of potential mixing (Starrfield et al. 2020, 2024). Our analysis suggests that in the case of V1716 Sco (which has a CO WD), a fraction of 25% rather than 50% is favored for the mixing between WD matter and the accreted envelope before the outburst. This is similar to the 25% mixing fraction that is favored in ONe novae (Kelly et al. 2013) and elsewhere. Acknowledgements The authors wish to acknowledge the referee for their insight and constructive critiques that improved the manuscript. The authors also are deeply indebted to Dr. D. P. K. Banerjee for his in depth discussion that paved the way for the analysis and interpretation of these data. We also acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. The optical spectroscopic data from ARAS site (Astronomical Ring for Amateur Spectroscopy) was helpful in our analysis. We are most grateful to Paul Kuin for exploring the availability of Swift UV spectra contemporaneous with the near-IR observations. GS acknowledges a WOS-A grant from the Department of Science and Technology (SR/WOS-A/PM2/2021). KLP acknowledges funding from the UK Space Agency. We thank John Rayner, Director IRTF, for Director\u2019s Discretionary Time (2023B988) who made scheduling of this program possible and the IRTF telescope operator for assisting CEW with the observations. The Infrared Telescope Facility, is operated by the University of Hawaii under contract 80HQTR19D0030 with the National Aeronautics and Space Administration. SS acknowledges partial support from a NASA Emerging Worlds grant to ASU (80NSSC22K0361) as well as support from his ASU Regents\u2019 Professorship. The x-ray data underlying this paper are available in the Swift archive at https://www.swift.ac.uk/swift live/ and the HEASARC Browse archive at https://heasarc.gsfc.nasa.gov/ cgi-bin/W3Browse/w3browse.pl. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https: //www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. Facilities: AAVSO, IRTF (SpeX), Swift, Gaia, DECaps Software: Astro Data Lab (Nikutta et al. 2020), Astropy (Astropy Collaboration et al. 2018), CLOUDY (Ferland et al. 1998; Chatzikos et al. 2023), Spextool (Cushing et al. 2004), HEASOFT/XSPEC (Arnaud 1996). V1716 SCO IR CORONAL ABUNDANCES 15 3000 2000 1000 0 1000 2000 3000 Velocity (km s 1) 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Continuum Normalized Relative Flux a) OI_0.8446 OI_1.1287 H I (P9)_0.9229 3000 2000 1000 0 1000 2000 3000 Velocity (km s 1) 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Continuum Normalized Relative Flux b) [Si X]_1.4301 u.i._1.5595 H I Br _2.1655 3000 2000 1000 0 1000 2000 3000 Velocity (km s 1) 0 2 4 6 8 10 12 14 16 18 Continuum Normalized Relative Flux c) [Mg VII]_3.0276 [Si IX]_3.9282 H I Br _4.0523 3000 2000 1000 0 1000 2000 3000 Velocity (km s 1) 0 2 4 6 8 10 Continuum Normalized Relative Flux -950 km/s -140 km/s +400 km/s +950 km/s H I (P9)_0.9229 [2.0x] H I Br _2.1655 [2.5x] H I Br _4.0523 Figure 7. Emission line velocity profiles of V1716 Sco on day +132.8. Each emission line is normalized to the average adjacent continuum and scaled (as indicated in the inset). The vertical black dashed line in each panel is 0 km s\u22121, and the \u2018u.i.\u2019 label indicates unidentified line. a) Lines of neutral oxygen O I 0.8446 and 1.1287 \u00b5m versus H I (P9) 0.9229 \u00b5m. b) Coronal lines of [Si IX] versus H I Br\u03b3 in the SpeX SXD mode. c) Coronal lines [Mg VII] and [Si IX] in the thermal IR (\u03bb > \u223c3.0 \u00b5m) versus H I Br\u03b1 in the SpeX LXD short mode. The FWHM of the [Mg VIII] profile is \u22433400 km s\u22121. d) Common velocity components present in the H I recombination line profiles (vertical black arrows). He+ He H+ H HeH+ Density (cm-3) 10\u22126 10\u22123 1 1000 106 109 Depth into the ejecta (cm) 1011 1012 1013 1014 1015 Figure 8. CLOUDY derived number densities (cm\u22123) of HeH+ (red) and that of of He (blue) and H+ (black) as a function of depth into the nova ejecta (cm) in V1716 Sco (+133 d). The ionization front is near \u22436 \u00d7 1013 cm. 16 WOODWARD ET AL."
+        },
+        {
+            "url": "http://arxiv.org/abs/2404.12141v2",
+            "title": "MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space",
+            "abstract": "Generative models for structure-based drug design (SBDD) have shown promising\nresults in recent years. Existing works mainly focus on how to generate\nmolecules with higher binding affinity, ignoring the feasibility prerequisites\nfor generated 3D poses and resulting in false positives. We conduct thorough\nstudies on key factors of ill-conformational problems when applying\nautoregressive methods and diffusion to SBDD, including mode collapse and\nhybrid continuous-discrete space. In this paper, we introduce MolCRAFT, the\nfirst SBDD model that operates in the continuous parameter space, together with\na novel noise reduced sampling strategy. Empirical results show that our model\nconsistently achieves superior performance in binding affinity with more stable\n3D structure, demonstrating our ability to accurately model interatomic\ninteractions. To our best knowledge, MolCRAFT is the first to achieve\nreference-level Vina Scores (-6.59 kcal/mol) with comparable molecular size,\noutperforming other strong baselines by a wide margin (-0.84 kcal/mol).",
+            "authors": "Yanru Qu, Keyue Qiu, Yuxuan Song, Jingjing Gong, Jiawei Han, Mingyue Zheng, Hao Zhou, Wei-Ying Ma",
+            "published": "2024-04-18",
+            "updated": "2024-04-23",
+            "primary_cat": "q-bio.BM",
+            "cats": [
+                "q-bio.BM",
+                "cs.LG"
+            ],
+            "label": "Original Paper",
+            "paper_cat": "Diffusion AND Model",
+            "gt": "Structure-based drug design (SBDD) advances drug dis- covery by leveraging 3D structures of biological targets, thereby facilitating efficient and rational design of molecules within a certain chemical space of interests (Wang et al., 2022; Isert et al., 2023). In recent years, the generative model for molecules has emerged as a promising direction, which could streamline SBDD by directly proposing desired molecules, eliminating the need for exhaustive blind search in the vast space (Walters, 2019; Luo et al., 2021). Re- *Equal contribution 1University of Illinois Urbana-Champaign, USA 2Department of Computer Science and Technology, Ts- inghua University 3Institute for AI Industry Research (AIR), Tsinghua University 4Shanghai Institute of Materia Med- ica, Chinese Academy of Sciences. Correspondence to: Jingjing Gong <gongjingjing@air.tsinghua.edu.cn>, Hao Zhou <zhouhao@air.tsinghua.edu.cn>. Preprint. Copyright 2024 by the author(s). cent progress in SBDD can be divided into two categories, i.e. auto-regressive models (Luo et al., 2021; Peng et al., 2022; Zhang et al., 2023) as next-token prediction for text generation, and diffusion models (Guan et al., 2022; 2023) as for image generation. The essential criteria for drug-like candidate molecules are outlined as follows: (i) high affinity towards specific binding sites (a.k.a, protein pockets), where a higher affinity indi- cates better performance, (ii) satisfactory drug-like prop- erties, such as synthesizability and drug-likeness scores, which often serve as thresholds for filtering out unfavor- able compounds (Ursu et al., 2011; Tian et al., 2015), and (iii) well-conformational 3D structure, which needs special attention for SBDD models, because they risk generating unrealistic molecular 3D conformations yet with deceptively high affinities. However, current generative models focus primarily on (i) and (ii), whereas we observe that the generated molecules often fail to meet all criteria simultaneously, especially for (iii) conformational stability. This challenge manifests as the False Positives phenomenon (FP) in generative modeling of SBDD, where models yield molecules that reside outside the true molecular manifold yet appear to exhibit good binding affinity after redocking. Specifically, these molecules suffer from distorted structure, displaying problematically unusual topology, and inferior binding mode, whereby the generated poses fail to capture true interactions and may even violate biophysical constraints, and thus go through post-fixes and significant rearrangements from docking software. Such problems threaten to jeopardize reliable model assessment, ultimately hindering their application in SBDD (Sec. 2.1). Both autoregressive and diffusion-based models exhibit chal- lenges with generating accurate molecular conformations, yet these issues stem from distinct causes. In Sec. 2.2, we delve into the mode collapse issue faced by autoregressive methods. Empirically, they tend to repeatedly generate a limited number of specific (sub-)structures due to an unnat- ural atom ordering imposed during generation. On the other hand, the problem with diffusion-based models is attributed to denoising in hybrid yet highly twisted space, which is a blend of discrete atomic types and continuous atomic coor- dinates. Different modalities need to be carefully handled 1 arXiv:2404.12141v2  [q-bio.BM]  23 Apr 2024 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space (a) Distorted Geometry AR strain: 653 kcal/mol strain: 700 kcal/mol DecompDiff strain: 1052 kcal/mol TargetDiff (b) Sub-optimal Binding FLAG RMSD: 5.11\u00a0\u00c5 DecompDiff RMSD: 7.73\u00a0\u00c5 Pocket2Mol RMSD: 6.66\u00a0\u00c5 (c) Generation Failure FLAG TargetDiff Figure 1: Typical resulting implausible molecules from gen- erative models. (a) Unusual 3-membered rings generated by AR, large fused rings with more than 7 atoms generated by diffusion models. (b) Examples of steric clashes by FLAG, and other ligand undergoing significant conformational rear- rangements upon redocking (Before: blue. After: green). (c) Failures in generation process. Left: atoms mis-connected in autoregressive sampling. Right: incomplete molecules with multiple components. in the hybrid space, and lack of consideration might result in severely strained and infeasible outputs (Sec. 2.3). Notably, DecompDiff (Guan et al., 2023) proposes to in- ject the molecular inductive bias by manually decomposing ligands into arms and scaffolds priors before training, and utilizing validity guidance in sampling. However, it cannot fully address the ill-conformational problem, since the in- ductive bias is simply impossible to enumerate. As shown in Fig. 2, for common C-N and C-O bond with two modes of typical length distribution, nearly all SBDD models are struggling to fit this substructural pattern. More visualiza- tion results can be referred to in Fig. 8, 9, 10, Appendix D. In order to capture the complicated data manifold for molecules, we take a shift to a unified continuous parameter space instead of a hybrid space, inspired by Graves et al. (2023). We propose MolCRAFT (Continuous paRAmeter space Facilitated molecular generaTion), which not only alleviates the mode collapse issue by non-autoregressive generation as in its diffusion counterparts, but also addresses the continuous-discrete gap by applying continuous noise and smooth transformation, leading to high-affinity as well as well-conformational drug candidates. Our contributions can be summarized as follows: \u2022 We investigate the false positive phenomenons of cur- rent SBDD models, and identify several key problems including the mode collapse of autoregressive meth- ods, and the gap of continuous-discrete space when applying diffusion models. \u2022 We propose MolCRAFT to address these two issues, which is a unified SE-(3) equivariant generative model, equipped with sampling in the parameter space that avoids further noise. \u2022 We conduct comprehensive evaluation under controlled molecular sizes. Experiments show that our model generates high-affinity binders with feasible 3D poses. To our best knowledge, we are the first to achieve reference-level Vina Scores (-6.59 kcal/mol, com- pared to reference -6.36 kcal/mol) with comparable molecule size, outperforming other strong baselines by a wide margin (-0.84 kcal/mol).",
+            "main_content": "We provide an overview of current obstacles in pocket-based generation. We summarize common failures in Sec. 2.1, and then investigate the underlying problems, i.e. the mode collapse issue of autoregressive-based models in Sec. 2.2, and hybrid denoising issue of diffusion-based models in Sec. 2.3. Based on the aforementioned challenges, we propose to generate molecules in the continuous parameter space. 2.1. Failure Modes of Generated Molecules As shown in Fig. 1, we divide undesired molecules in SBDD into three categories: (a) Distorted geometry. We visualize the generated molecules at median strain energy (see Table 2), and models tend to produce either too many uncommon 3or 4-member rings, or extra-large rings with unstable structures, leading to much higher strain energy. (b) Inferior binding mode. We observe a notable number structures, leading to much higher strain energy. (b) Inferior binding mode. We observe a notable number of generated ligand conformations rearrange drastically after redocking, with some even violating biophysical constraints and producing steric clashes with the protein surface. This suggests that 3D SBDD models do not capture true interatomic interactions and rely on post-fixing via redocking as noted by Harris et al. (2023), which severely harms the credibility of generating molecules directly in 3D space. (c) Generation failure. Autoregressive models tend to ating molecules directly in 3D space. (c) Generation failure. Autoregressive models tend to misplace an element and terminate prematurely, while diffusion models might generate incomplete molecules with disconnected parts, limiting sample efficiency. The above problems hinder the applicability of SBDD models. In the following sections, we provide deeper understanding of the problematic methods underlying these failures. 2 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Density Reference CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Density AR CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.00 0.02 0.04 0.06 Density Pocket2Mol CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.0 0.1 0.2 0.3 0.4 0.5 Density FLAG CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.00 0.05 0.10 0.15 Density T argetDiff CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.000 0.025 0.050 0.075 0.100 0.125 0.150 Density DecompDiff-O CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.000 0.025 0.050 0.075 0.100 0.125 0.150 Density DecompDiff-R CC C:C CO CN C:N 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Bond length (\u00c5) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Density Ours CC C:C CO CN C:N Figure 2: Bond length distribution of reference and generated molecules by autoregressive models (upper row) and nonautoregressive models (lower row) for top-5 frequent bond types. Table 1: Percentage (%) of molecular modes in terms of distribution and substructures. Note: Fused refers to 80 specific rings, 3-Ring denotes three-membered rings, and so on. Highly deviated values are highlighted in bold Italic. Unique Fused 3-Ring 4-Ring 5-Ring 6-Ring Reference 30.0 4.0 0.0 49.0 84.0 Train 21.6 3.8 0.6 56.1 90.9 AR 36.2 39.7 50.8 0.8 35.8 71.9 Pocket2Mol 73.7 52.0 0.3 0.1 38.0 88.6 FLAG 99.7 42.4 3.1 0.0 39.9 84.7 TargetDiff 99.6 37.8 0.0 7.3 57.0 76.1 Decomp-O 61.6 13.1 9.0 11.4 64.0 83.3 Decomp-R 50.3 28.1 5.4 8.3 51.5 65.6 Ours 97.7 30.9 0.0 0.6 47.0 85.1 2.2. Molecular Mode Collapse The mode collapse issue focuses on the empirical performance of SBDD methods that tend to generate a limited number of specific (sub-)structures, where atom-based autoregressive models have displayed a particular preference for certain modes. We provide quantitative results from both the chemical and geometrical perspectives. Chemical assessment is shown in Table 1. In order to measure molecular distribution, we report the percentage of unique samples (Unique) averaged on different pockets.1 It can be seen that the ratio of unique molecules of AR (Luo et al., 2021) and Pocket2Mol (Peng et al., 2022) is considerably lower than other counterparts. Moreover, DecompDiff (Guan et al., 2023) is also found to generate repeated molecules, possibly due to its use of prior clusters At the substructural level, we report the percentage of molecules with certain types of rings defined by Jiang et al. (2024), 1Here we remove all post-filters from autoregressive models that avoid generating duplicate or invalid molecules, in order to faithfully demonstrate their performances. In all other experiments, we stick to the original implementation. with respect to all ring-structured molecules. Pocket2Mol displays a preference for more fused rings as also noted by Harris et al. (2023), while AR exhibits an obvious pattern in generating repeated three-membered rings. Geometrically measured, as shown in Fig. 2, atom-based autoregressive methods model the bond lengths for different bond types similarly, where reference distribution is multimodal and varies across different types, while Pocket2Mol only captures a single mode, and for AR different bond lengths are distributed in a very similar fashion. FLAG (Zhang et al., 2023) generates fragment-by-fragment, which avoids collapsing by explicitly incorporating optimal and diverse substructures. But it suffers from more severe error accumulation, resulting in significant steric clashes and undesirable Vina Score (see Sec. 5.2). Generally speaking, autoregressive models are still trapped in sub-optimal performance. Intuitively, such limitations could be attributed to an unnatural atom ordering imposed during generation. 0.0 0.2 0.4 0.6 0.8 1.0 Generative Process 0.0 0.2 0.4 0.6 0.8 1.0 Validity ( ) 0.0 0.2 0.4 0.6 0.8 1.0 Generative Process 0.0 0.2 0.4 0.6 0.8 1.0 Completeness ( ) T argetDiff Decomp-O Decomp-R Ours Figure 3: Percentage of valid, complete molecules in the trajectories during generative process. 2.3. Hybrid Continuous-Discrete Space Diffusion-based models, on the other hand, successfully alleviate mode collapse problem via non-autoregressive generation in terms of substructural distribution (see Fig. 2). However, the inconsistency between different modalities has 3 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space SE-(3) NN \u00a0 KL-div Update \u00a0 Parameter Space ...... Add Noise Reduce Noise Add Noise Sample Space Figure 4: Overall Architecture. long troubled molecular generation models, as suggested by MolDiff (Peng et al., 2023) and EquiFM (Song et al., 2024b), where a careful design of either different noise levels or different probability paths is required. A key insight is that the hybrid continuous-discrete space poses challenges to accurately capture the complicated data manifold for molecules, where the sample space in diffusion models is exposed to high variance, and the intermediate noisy latent is very likely to go outside the manifold. Inspired by GeoBFN (Song et al., 2024a), we propose to operate within the fully continuous pamarater space, which enables considerably lower input variance and a smooth transformation towards the target distribution. To further illustrate the difference between continuousdiscrete diffusion and our fully continuous MolCRAFT, we sample 10 molecules for each of the 100 test proteins, and plot the curves of the ratio of valid molecules, complete molecules against different timesteps during sampling. As shown in Fig. 3, continuous-discrete diffusions heavily rely on the latter steps, passing a certain validity and completeness threshold in the final 60%-90% stage where noise scales are lower, while MolCRAFT approaches target distribution far earlier (in the first 20%-40% steps), thereby possessing greater capacity to progressively refine and adjust the generated feasible structures, resulting in better conformations. 3. Preliminary In this section, we briefly overview Bayesian Flow Networks (BFN) (Graves et al., 2023) in comparison with diffusion models for SBDD. For its detailed formulation and mathematical details, we refer readers to Appendix A. 3.1. Problem Definition Structure-based Drug Design (SBDD) can be formulated as a conditional generation task. Given input protein binding site P = {(x(i) P , v(i) P )}NP i=1, which contains NP atoms with each x(i) P \u2208R3 and v(i) P \u2208RDP correspond to atom coordinates and atom features, respectively (e.g., element types, backbone or side chain indicator). The output is a ligand molecule M = {(x(i) M , v(i) M )}NM i=1, where x(i) M \u2208R3 and v(i) M \u2208RDM , NM is the number of atoms in molecule. For convenience, we denote p = [xP , vP ], (xP \u2208RNP \u00d73, vP \u2208RNP \u00d7DP ) and m = [xM, vM], (xM \u2208RNM\u00d73, vM \u2208RNM\u00d7DM ) as the concatenation of all protein or ligand atoms. 3.2. Molecular Generation in Parameter Space The overall architecture of MolCRAFT are shown in Fig. 4. The generative process is viewed as message exchanges between a sender and a receiver, where the sender is only visible in sample space, and the receiver makes the guess from its understanding of samples and parameters. In every round of communication, the sender selects a molecule datapoint m, adds noise for timestep ti according to sender distribution pS(yi | m; \u03b1i), and sends the noisy latent y to receiver, resembling the forward diffusion process. Here \u03b1i is a noise factor from the schedule \u03b2(ti). The receiver, on the other hand, outputs the reconstructed molecule \u02c6 m based on its previous knowledge of parameters \u03b8, yielding output distribution pO. With the sender\u2019s noisy factor \u03b1 known, the receiver can also add noise to the estimated output and give the predicted noisy latent, arriving at receiver distribution pR. pR(yi | \u03b8i\u22121, p; ti) = E \u02c6 m\u223cpOpS(yi | \u02c6 m; \u03b1i), (1) where pO( \u02c6 m | \u03b8i\u22121, p; ti) = \u03a6(\u03b8i\u22121, p, ti). (2) \u03a6 is a neural network which is expected to reconstruct clean sample \u02c6 m given parameters \u03b8i\u22121, pocket p and time ti. The key difference between BFN and diffusion lies in its introduction of parameters. Thanks to structured Bayesian updates defined via Bayesian inference, the receiver is able to maintain fully continuous parameters and perform closedform update on its belief of parameters. Bayesian update distribution pU stems from the Bayesian update function h, pU(\u03b8i | \u03b8i\u22121, m, p; \u03b1i) = E y\u2032 i\u223cpS \u03b4 \u0010 \u03b8i \u2212h(\u03b8i\u22121, yi, \u03b1i) \u0011 , (3) where \u03b4(\u00b7) is Dirac delta distribution. The parameter space enables arbitrarily applying noise as long as the Bayesian update is tractable, and eliminates the need to invert a predefined forward process as in diffusion models. According to the nice additive property of accuracy (Graves et al., 2023), the Bayesian flow distribution pF could be obtained to achieve simulation-free training, once teacher 4 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space forcing with m is applied: pF (\u03b8i | m, p; ti) = E \u03b81...i\u22121\u223cpUpU(\u03b8i | \u03b8i\u22121, m, p; \u03b1i) = pU(\u03b8i | \u03b80, m, p; \u03b2(ti)) (4) Therefore, the training objective for n steps is to minimize: Ln(m, p) = E i\u223cU(1,n) E yi\u223cpS,\u03b8i\u22121\u223cpFDKL(pS \u2225pR). (5) 4. Methodology We introduce our proposed MolCRAFT in as follows: in Sec. 4.1, we demonstrate how to model continuous atom coordinates and discrete atom types within BFN framework, with the guarantee of SE-(3) equivariance for molecular data. Then in Sec. 4.2, we elaborate our novel sampling strategy tailored for the parameter space. Within the fully continuous and differentiable space, MolCRAFT is able to capture the global connection between different modalities, and sample efficiently with low variance. 4.1. Resolving Different Modalities in Parameter Space This section demonstrates how to resolve continuous atom coordinates and discrete atom types in parameter space. Unified parameter \u03b8 def := [\u03b8x, \u03b8v] Following Hoogeboom et al. (2022), continuous atom coordinates x are characterized by Gaussian distribution N(x | \u00b5, \u03c1\u22121I), and we set \u03b8x = {\u00b5, \u03c1}, where \u00b5 is learned and \u03c1 is predefined by noise factor \u03b1. The Bayesian update function {\u00b5i, \u03c1i} \u2190h( \b \u00b5i\u22121, \u03c1i\u22121 \t , yx, \u03b1i) is defined as: \u03c1i = \u03c1i\u22121 + \u03b1i (6) \u00b5i = \u00b5i\u22121\u03c1i\u22121 + yx\u03b1i \u03c1i (7) For discrete atom types v, we use a categorical distribution \u03b8v \u2208RNM\u00d7K, and update it given \u03b1\u2032 via h(\u03b8v i\u22121, yv, \u03b1\u2032 i) def := eyv\u03b8v i\u22121 PK k=1 eyv k(\u03b8v i\u22121)k (8) For prior \u03b80, we adopt standard Gaussian and uniform distribution respectively, following Graves et al. (2023). Applying noise for different modalities Thanks to the continuous nature of parameters, we are able to apply the following continuous noise even for discrete atom types, instantiating the sender distribution pS: pS(yx | xM; \u03b1) = N(yx | xM, \u03b1\u22121I) (9) pS(yv | vM; \u03b1\u2032) = N \u0010 yv | \u03b1\u2032(KevM \u22121), \u03b1\u2032KI \u0011 (10) where evM = h ev(1) M , . . . , ev(K) M i \u2208RNM\u00d7K, ej \u2208RK is the projection from the class index j to the length-K one-hot vector, and K the number of atom types. Note that we could set different noise schedules for different modalities (\u03b1 for coordinates and \u03b1\u2032 for types) for more efficient training of the joint noise prediction network. Thereby for receiver distribution in Eq. 1, pR(yx | \u03b8x, p; t) = N(yx | \u03a6(\u03b8x, p, t), \u03b1\u22121I) (11) pR(yv | \u03b8v, p; t) = h pR \u0000(yv)(d)| \u00b7 \u0001i d=1...N, (12) where pR \u0010 (yv)(d)| \u00b7 \u0011 = P k pv O(k|\u00b7)pv S \u0010 (yv)(d)|k; \u03b1 \u0011 . SE-(3) equivariance We introduce a fundamental inductive bias for SBDD to BFN, i.e. the density should be invariant to translation and rotation of protein-molecule complex (Satorras et al., 2021; Xu et al., 2021; Hoogeboom et al., 2022), in the following proposition (proof in Appendix B). Proposition 4.1. Denote the SE-(3) transformation as Tg, the likelihood is invariant w.r.t. Tg on the protein-molecule complex: p\u03d5(Tg(m|p)) = p\u03d5(m|p) if we shift the Center of Mass (CoM) of protein atoms to zero and parameterize the output network \u03a6(\u03b8, p, t) with an SE-(3) equivariant network. 4.2. Noise Reduced Sampling in Parameter Space MolCRAFT addresses the high-variance discrete variable problem by maintaining a continuous probability mass function as beliefs of distributional parameters, which allows a smooth transformation towards the target distribution. This natural coherence with continuous coordinates gives us an advantage over continuous-discrete diffusion process. During sampling, original BFN shifts the denoising process from sample space (recall diffusion yi\u22121 \u2192yi) to parameter space (\u03b8i\u22121, yi) \u2192\u03b8i via Bayesian update function h, where the information flows in this direction: \u03b8i\u22121 \u03a6 \u2212 \u2192\u02c6 m pS \u2212 \u2192yi pU \u2212 \u2212 \u2192\u03b8i, (13) where pU(\u03b8i | \u03b8i\u22121, m, p; \u03b1i) is defined in Eq. 3, and m is set to estimated \u02c6 m drawn from pO in Eq. 2. It should be noted that the existing generative process of BFN, as well as that of diffusion models, performs continuous atom coordinates and discrete atom type sampling at each timestep. This risks introducing too much noise, and might end up generating incomplete molecules. To alleviate such a problem, we design an empirically effective sampling strategy, which operates within the parameter space, and thus avoids introducing further noise from sampling discrete variables. The graphical description becomes: 5 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space \u03b8i\u22121 \u03a6 \u2212 \u2192\u02c6 m pF \u2212 \u2212 \u2192\u03b8i (14) Specifically, denoting \u03b3(t) def := \u03b2(t) 1\u2212\u03b2(t), we update the parameter via Eq. 4, which simplifies to: pF (\u00b5 | \u02c6 x, p; t) = N \u0010 \u00b5 | \u03b3(t)\u02c6 x, \u03b3(t)(1 \u2212\u03b3(t))I \u0011 (15) pF (\u03b8v | \u02c6 v, p; t) = E N \u0000yv|\u03b2(t)(Ke\u02c6 v\u22121),\u03b2(t)KI \u0001\u03b4(\u03b8v \u2212softmax(yv)) (16) We use the estimated \u02c6 m = [\u02c6 x, \u02c6 v] (note that \u02c6 v directly takes the continuous output categorical values without sampling) to directly update parameter for the next step, bypassing the sampling of noisy data needed for Bayesian update \u03b8i = h(\u03b8i\u22121, y, \u03b1). The whole generative process happens in the parameter space except for the final step, which enjoys the advantage of lower variance and accelerates the overall generation path towards the complicated structure of molecules, with greatly improved sample quality at significantly fewer sampling steps, as shown in Fig. 7. Details of sampling are described in Algorithm 2. 5. Experiments 5.1. Experimental Setup Dataset We use the CrossDocked dataset (Francoeur et al., 2020a) for training and testing, which originally contains 22.5 million protein-ligand pairs, and after the RMSD-based filtering and 30% sequence identity split by Luo et al. (2021), results in 100,000 training pairs and 100 test proteins. For each test protein, we sample 100 molecules for evaluation. Baselines For autoregressive sampling-based models, we choose atom-based models AR (Luo et al., 2021), Pocket2Mol (Peng et al., 2022) and fragment-based model FLAG (Zhang et al., 2023). For diffusion-based models, we consider TargetDiff (Guan et al., 2022) and two variants of DecompDiff (Guan et al., 2023). Decomp-R uses the prior estimated from reference molecules in the test set, while Decomp-O selects the optimal prior from the reference prior and pocket prior, where the pocket prior center is predicted by AlphaSpace2 (Katigbak et al., 2020) and ligand atom number by a neural classifier. Evaluation We conduct a comprehensive evaluation of SBDD models on all 100 proteins in test set, including: \u2022 Binding Affinity. We employ AutoDock Vina (Trott & Olson, 2010) to measure binding affinity as it is a common practice (Luo et al., 2021; Peng et al., 2022; Guan et al., 2022; 2023), and report Vina Score, a direct score of generated pose, Vina Min, which scores the optimized pose after a local minimization of energy, and Vina Dock, the best possible score after re-docking, a global grid-based search optimization process. Therefore, it is highly favorable if Vina Score is close to Vina Min and Vina Dock, suggesting that the generated poses capture the 3D interaction well. \u2022 Conformation Stability. We measure the stability for ligand-only and binding complex conformation. For ligand-only, we use the Jensen-Shannon divergence (JSD) between reference and generated distributions of bond length, bond angle and torsion angle at substructure level, and for a more global view, we employ Strain Energy to evaluate the rationality of generated ligand conformation. For binding complex, we adopt Steric Clashes (Clash) to detect possible clashes in protein-ligand complex, following Harris et al. (2023). We further propose to evaluate symmetry-corrected RMSD between the generated ligand atoms and Vina redocked poses as the metric of binding mode consistency, where poses with an RMSD below 2 \u02da A is generally regarded as chemically meaningful (Alhossary et al., 2015; Hassan et al., 2017; McNutt et al., 2021). \u2022 Drug-like Properties. Drug-likeliness (QED), synthetic accessibility (SA), and diversity (Div) are adopted as molecular property metrics. \u2022 Overall. To evaluate the overall quality of generated molecules, we calculate the Binding Feasibility as the ratio of molecules with reasonable affinity (Vina Score < -2.49 kcal/mol) and stable conformation (strain energy < 836 kcal/mol, RMSD < 2 \u02da A) simultaneously, where the threshold values are set to the 95 percentile of the reference molecules. We also report Success Rate (Vina Dock < -8.18, QED > 0.25, SA > 0.59) following Long et al. (2022) and Guan et al. (2022). \u2022 Sample Efficiency. In order to make a practical comparison among non-autoregressive methods, we report the average Time and Generation Success, with the latter defined as the ratio of valid and complete molecules versus the intended number of samples. 5.2. Main Results Our main findings are listed as below: \u2022 MolCRAFT resembles and even surpasses the reference set in terms of binding affinity and overall feasibility, showing that we effectively learn the binding dynamics from protein-ligand complex distribution. \u2022 Non-autoregressive molecule generation could benefit from modeling in continuous parameter space, demonstrated by our performance in capturing diverse substructural modes and greatly improved conformation. \u2022 Reliable evaluation of SBDD ought to take molecule sizes into account. To achieve fair comparison, controlled experiment regarding molecule size is needed. 6 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space Table 2: Summary of different properties of reference and generated molecules under different sizes. (\u2191) / (\u2193) indicates larger / smaller is better. Top 2 results are highlighted with bold text and underlined text. Note: SE is short for Strain Energy, Div for Diversity, BF for Binding Feasibility, and SR for Success Rate. Methods Binding Affinity Conformation Stability Drug-like Properties Overall Ligand Complex Vina Score (\u2193) Vina Min (\u2193) Vina Dock (\u2193) SE (\u2193) Clash (\u2193) RMSD (\u2191) SA (\u2191) QED (\u2191) Div (\u2191) BF (\u2191) SR (\u2191) Size Avg. Med. Avg. Med. Avg. Med. 25% 75% Avg. % < 2 \u02da A Avg. Avg. Avg. (%) (%) Avg. Reference -6.36 -6.46 -6.71 -6.49 -7.45 -7.26 38 198 5.57 34.0 0.73 0.48 26.0 25.0 22.8 AR -5.75 -5.64 -6.18 -5.88 -6.75 -6.62 260 2287 4.36 36.5 0.63 0.51 0.70 16.1 6.9 17.7 Pocket2Mol -5.14 -4.70 -6.42 -5.82 -7.15 -6.79 102 373 6.10 32.0 0.76 0.57 0.69 23.8 24.4 17.7 FLAG 45.85 36.52 9.71 -2.43 -4.84 -5.56 25 4384 68.55 0.3 0.63 0.61 0.70 0.0 1.8 16.7 Ours-small -5.96 -5.89 -6.34 -6.04 -6.98 -6.63 44 275 4.77 39.5 0.74 0.52 0.74 33.3 17.4 17.8 TargetDiff -5.47 -6.30 -6.64 -6.83 -7.80 -7.91 368 13527 11.13 37.1 0.58 0.48 0.72 13.5 10.5 24.2 Decomp-R -5.19 -5.27 -6.03 -6.00 -7.03 -7.16 111 1217 7.92 24.2 0.66 0.51 0.73 14.6 14.9 21.2 Ours -6.59 -7.05 -7.24 -7.26 -7.80 -7.92 84 517 7.02 46.1 0.69 0.50 0.72 35.9 26.0 22.7 Decomp-O -5.67 -6.04 -7.04 -7.09 -8.39 -8.43 368 3876 13.76 27.2 0.61 0.45 0.68 11.1 24.5 29.4 Ours-large -6.61 -8.16 -8.14 -8.45 -9.21 -9.22 174 1079 10.87 45.0 0.62 0.46 0.61 31.1 36.6 29.4 Table 3: Summary of molecular conformation results. (\u2193) indicates smaller is better. Top 2 results are highlighted with bold text and underlined text. Note: JSD is calculated between distributions estimated from generated and reference molecules, we report the mean of all JSD values here. Methods Length (\u2193) Angle (\u2193) Torsion (\u2193) Avg. JSD Avg. JSD Avg. JSD AR 0.554 0.507 0.552 Pocket2Mol 0.485 0.482 0.459 FLAG 0.511 0.406 0.270 TargetDiff 0.382 0.435 0.400 Decomp-O 0.359 0.414 0.358 Decomp-R 0.348 0.412 0.317 Ours 0.319 0.379 0.300 Binding Affinity We report Vina metrics in Table 2. I. Our model consistently outperforms other strong baselines in affinities, achieving a reference-level Vina Score of -6.59 kcal/mol. As Vina Score directly scores the pose and Vina Min only optimizes locally, they directly measure the generated pose quality. To the best of our knowledge, MolCRAFT is the first to achieve reference-level affinity scores without significant rearrangements via redocking, which demonstrates our superiority in learning binding interactions for SBDD. II. Vina Dock can potentially be hacked by generating larger molecules. Intuitively, larger molecules have more chances of forming interactions with protein surfaces. With the largest molecule sizes, Decomp-O achieves the secondbest Vina Dock (-8.39 kcal/mol), far better than reference molecules. Further investigation reveals that Decomp-O gains an advantage by producing considerably larger outof-distribution (OOD) molecules and thereby brings up the highest possible affinity post-docking. For a fair comparison, we report variants of DecompDiff and MolCRAFT stratified by size, and with the same number of atoms as Decomp-O, our model consistently achieves SOTA affinities, underscoring its robustness across different molecular sizes. Conformation Stability We report the substructural level\u2019s average Jensen-Shannon divergence (JSD) between reference and generated bond length, angle and torsion angle distributions in Table 3 (detailed results for different bond/angle/torsion types in Appendix D). At the global structure level, we report strain energy for ligand-only conformational stability, and measure clashes in the binding complex, together with RMSD between generated and redocked poses in Table 2. I. Our model excels in modeling diverse local modes, and ranks first in bond length and angle distributions. Moreover, Fig. 2 shows MolCRAFT is the only model that captures two distinct modes for multi-modal C-C, C-N and C-O bond, justifying our choice of modeling in the joint continuous parameter space. More results are in Fig. 8, 9 and 10. II. Injecting substructural inductive bias helps to capture more modes. Fragment-based model FLAG displays the best torsion angle distribution, and prior-enhanced DecompDiff also exhibits relatively competitive performances in modeling molecular geometries, whereas other autoregressive models collapse into certain modes as in Fig. 2. III. For ligand-only stability, we greatly improve upon the strained conformations, even surpassing autoregressive methods. According to Table 2, our model is at least an order of magnitude better than diffusion-based counterparts, and is close to reference. While autoregressive methods generally display better strain energy, MolCRAFT still achieves superior performance under comparable molecule sizes. IV. Our binding complex contains fewer clashes and remains consistent after redocking. We achieve few steric clashes, and has the best RMSD performance, which means 46% of our molecules already resemble accurate docking pose even without force field optimization or redocking, rendering it reliable for generating molecules in 3D space. The reason why we achieve even better RMSD than reference could be explained by a distribution shift from the training set to the 7 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space 0.75 0.80 0.85 0.90 0.95 Generation Success 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 No. Generated Samples Per Second Ours AR Pocket2Mol FLAG T argetDiff Decomp-O Decomp-R Figure 5: Sample efficiency, where Generation Success means the generated molecules are both valid and complete. reference set. In the construction of dataset2, the training set contains 52.4% docked molecules, while the test set only contains 37.0% docked ones, which aligns with the phenomenon that there are only 34.0% reference molecules with RMSD < 2 \u02da A upon redocking. This accounts for why MolCRAFT has more consistent and high-affinity binders, which effectively captures the training set distribution and learns the binding dynamics. Overall We report the overall feasible rate and success rate in Table 2. MolCRAFT achieves the best among all, demonstrating our competency in generating molecules with high affinity and stable conformation. Our method captures the interatomic interactions in 3D space, and proposes desirable molecules without relying on post-fixed docking poses. This further validates our choice of learning in the continuous parameter space. Sampling performance We compare the generation speed (average time for generating 100 samples) and generation success in Figure 5. We achieve SOTA sampling performance in both dimensions, generating more complete (96.7%) molecules at 30\u00d7 speedup. While it takes on average 3428s and 6189s for TargetDiff and DecompDiff to generate 100 samples respectively, our model only uses 141s, thanks to our improved sampling strategy (see Sec. 5.3). 5.3. Ablation Study of Sampling Strategy Considering that we propose the first-of-its-kind SBDD model that operates in the fully continuous parameter space, and present a noise-reduced sampling approach adapted to the space, we conduct ablation study that validates our design, showing a performance boost from Vina Score/Min of -5.42/-6.30 kcal/mol to -6.51/-7.13 kcal/mol. 2There are two kinds of 3D ligand poses in the dataset, i.e. Vina minimized poses in the given receptor, and Vina docked poses. https://github.com/gnina/models/ tree/master/data/CrossDocked2020 We test different sampling strategies with different steps for the same checkpoint, and sample 10 molecules each for 100 test proteins. We plot the curves of QED, SA, Completeness (\u2191) and Vina Score (\u2193) in Figure 7, Appendix D.2. As the sampling step increases to training steps, we found the original sampling strategy exhibits first enhanced then slightly decreased sample quality, possibly because the update of parameters is smoothed or oversmoothed by finer partitioned noise factor \u03b1, whereas the noise reduced strategy displays this tendency far earlier and generates the best quality of molecules with fewer sampling steps, indicating its high efficiency. Considering the overall sample quality, we decide to use 100 sampling steps for our model, which is 10\u00d7 faster than sampling at original 1000 training steps. 6. Related Work Target-Aware Molecule Generation Trained on proteinligand complex data, target-aware methods directly model the interaction between protein pockets and ligands. Early attempts are based on 1D SMILES or 2D molecular graph generation (Bjerrum & Threlfall, 2017; G\u00b4 omez-Bombarelli et al., 2018; Segler et al., 2018) and fail to consider spatial information. Recent works focus on 3D molecule generation, and there are mainly two fashions: (1) Autoregressive methods. For atom-based methods, LiGAN (Masuda et al., 2020) and AR (Luo et al., 2021) adopt an atomic density grid view of molecules, the former predicting a voxelized density grid and performing optimization to reconstruct atom types and coordinates, the latter assigning atomic probability to each voxel and utilizes MCMC to generate atom-by-atom. GraphBP (Liu et al., 2022) uses normalizing flow and encodes the context to preserve 3D geometric equivariance, and Pocket2Mol (Peng et al., 2022) further adds bond generation for more realistic molecular structure. For fragment-based methods (Powers et al., 2022; Zhang & Liu, 2023; Zhang et al., 2023), molecules are decomposed into chemically meaningful motifs rather than seperated atom point cloud, and generated via motif assembling. (2) Diffusion-based methods have recently been proposed, aiming to overcome the problem of sampling efficiency and unnatural ordering brought by autoregressive fashion (Schneuing et al., 2022; Guan et al., 2022; 2023). But these methods still suffer from false positive problems. 7. Conclusion In this paper, we first investigate the challenges of current generative models in SBDD, i.e., distorted structures and sub-optimal binding modes. Based on the observations concerning mode collapse and hybrid space, we propose MolCRAFT, an SE-(3) equivariant generative model operating in the continuous parameter space with a noise reduced sampling strategy, which yields higher quality molecules. 8 MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space Broader Impact This paper is aimed to facilitate in-silico rational drug design. Potential society consequences include mal-intended usage of toxic compound discovery, which needs support from professional wet labs and thus expensive to reach. Therefore we do not possess a negative vision that this might lead to serious ethical consequences, though we are aware of such a possibility."
+        },
+        {
+            "url": "http://arxiv.org/abs/2404.07299v1",
+            "title": "JWST/MIRI detection of suprathermal OH rotational emissions: probing the dissociation of the water by Lyman alpha photons near the protostar HOPS 370",
+            "abstract": "Using the MIRI/MRS spectrometer on JWST, we have detected pure rotational,\nsuprathermal OH emissions from the vicinity of the intermediate-mass protostar\nHOPS 370 (OMC2/FIR3). These emissions are observed from shocked knots in a\njet/outflow, and originate in states of rotational quantum number as high as 46\nthat possess excitation energies as large as $E_U/k = 4.65 \\times 10^4$ K. The\nrelative strengths of the observed OH lines provide a powerful diagnostic of\nthe ultraviolet radiation field in a heavily-extinguished region ($A_V \\sim 10\n- 20$) where direct UV observations are impossible. To high precision, the OH\nline strengths are consistent with a picture in which the suprathermal OH\nstates are populated following the photodissociation of water in its $\\tilde B\n- X$ band by ultraviolet radiation produced by fast ($\\sim 80\\,\\rm km\\,s^{-1}$)\nshocks along the jet. The observed dominance of emission from symmetric\n($A^\\prime$) OH states over that from antisymmetric ($A^{\\prime\\prime}$) states\nprovides a distinctive signature of this particular population mechanism.\nMoreover, the variation of intensity with rotational quantum number suggests\nspecifically that Ly$\\alpha$ radiation is responsible for the photodissociation\nof water, an alternative model with photodissociation by a 10$^4$ K blackbody\nbeing disfavored at a high level of significance. Using measurements of the\nBr$\\alpha$ flux to estimate the Ly$\\alpha$ production rate, we find that $\\sim\n4\\%$ of the Ly$\\alpha$ photons are absorbed by water. Combined with direct\nmeasurements of water emissions in the $\\nu_2 = 1 -0$ band, the OH observations\npromise to provide key constraints on future models for the diffusion of\nLy$\\alpha$ photons in the vicinity of a shock front.",
+            "authors": "David A. Neufeld, P. Manoj, Himanshu Tyagi, Mayank Narang, Dan M. Watson, S. Thomas Megeath, Ewine F. Van Dishoeck, Robert A. Gutermuth, Thomas Stanke, Yao-Lun Yang, Adam E. Rubinstein, Guillem Anglada, Henrik Beuther, Alessio Caratti o Garatti, Neal J. Evans II, Samuel Federman, William J. Fischer, Joel Green, Pamela Klaassen, Leslie W. Looney, Mayra Osorio, Pooneh Nazari, John J. Tobin, Lukasz Tychoniec, Scott Wolk",
+            "published": "2024-04-10",
+            "updated": "2024-04-10",
+            "primary_cat": "astro-ph.GA",
+            "cats": [
+                "astro-ph.GA"
+            ],
+            "label": "Original Paper",
+            "paper_cat": "Diffusion AND Model",
+            "gt": "1. In the realm of molecular astrophysics, one of the most remarkable results obtained by Spitzer",
+            "main_content": "the detection of highly suprathermal OH rotational emissions. The observed transitions, detected with the Short-Hi module of the Infrared Spectrometer (IRS) toward the Herbig-Haro object HH 211 3 (Tappe et al. 2008), originate in pure rotational states with rotational quantum numbers N as high as 34 and energies as high as E/k = 2.8\u00d7104 K. They are naturally explained as the \u201cprompt emission\u201d that follows the photodissociation of water via the \u02dc B\u2212X band (also known as the \u201csecond absorption band\u201d) by radiation in the 114 \u2013 134 nm wavelength range; this spectral region includes the strong Ly\u03b1 line emitted by fast interstellar shocks. This explanation is supported by both laboratory and theoretical studies of water photodissociation through the \u02dc B \u2212X band, which indicate that OH states as high as N = 47 can be populated (Harich et al. 2000, van Harrevelt & van Hemert 2000). Suprathermal OH emissions resulting from the photodissociation of water were subsequently observed in protostellar disks with Spitzer: the protostellar disk of DG Tau, in particular, has been the subject of a detailed analysis by Carr & Najita (2014). Spitzer could not perform high-spectral resolution observations shortwards of 10\u00b5m, the short wavelength cuto\ufb00of the Short-Hi module of the IRS, and at shorter wavelengths the Short-Lo module on Spitzer/IRS provided a spectral resolving power, \u03bb/\u2206\u03bb, of only \u223c60, which was insu\ufb03cient to detect suprathermal OH emissions. By contrast, the MIRI MRS spectrometer on JWST provides coverage down to the OH band-head at 9.13 \u00b5m (and below), yielding spectra with a spectral resolving power \u223c3000. This unique capability opens up the possibility of detecting suprathermal OH emission in the 9 \u2013 10 \u00b5m range, a possibility that has been realized in observations of the Orion Bar reported very recently (Zannese et al. 2023), providing a powerful test of model predictions for the spectrum of the OH prompt emission (e.g. Tabone et al. 2021, hereafter T21). In this Letter, we discuss JWST/MIRI observations of suprathermal OH emissions in the vicinity of the protostar HOPS 370. HOPS 370, a.k.a. OMC2/FIR3, is an intermediate-mass Class 0/I protostar (Furlan et al. 2016). It is located north of the Orion Nebula in the OMC2 region of the integral shaped \ufb01lament at an estimated distance of 392 pc (Kounkel et al. 2018, Tobin et al. 2020, hereafter T20). Its central protostellar mass, determined from Keplerian motions, is 2.5 M\u2299, and its bolometric luminosity is 314 L\u2299(T20). Extensive observations of HOPS 370 have been carried out with multiple observatories \u2013 including Herschel, SOFIA, VLA, ALMA, and now JWST \u2013 and together reveal an actively accreting protostar with a bipolar jet/out\ufb02ow that is orthogonal to a rotating disk of 4 estimated mass 0.05 \u2013 0.1 M\u2299. It powers a large out\ufb02ow traced in millimeter and far-IR lines, which suggests that it is in a state of rapid accretion (T20; Manoj et al. 2013; Gonz\u00b4 alez-Garc\u00b4 \u0131a et al. 2016; Sato et al. 2023). This out\ufb02ow consists of both a wide-angle wind and a collimated jet, the latter containing shocks that are also seen in non-thermal radio emission (Osorio et al. 2017). The orientation of the disk, with an estimated radius of 100 au, indicates that this source is observed at a high inclination angle of \u223c72 \u25e6(T20; Federman et al. 2023, and references therein). Luminous shocked knots in the northern out\ufb02ow lobe are characterized by strong emissions from a variety of molecules and atomic ions detected in our observations, including H2, H2O, CO, OH, Fe+, and Ne+. In Section 2, we discuss the MIRI and NIRSpec observations carried out toward HOPS 370 and the methods used to reduce the data. The resultant spectra and spectral line maps are presented in Section 3, with particular emphasis on the suprathermal OH emissions from the shocked knots. The origin of those emissions is discussed in Section 4, in the context of a model in which water is photodissociated by shock-produced Ly\u03b1 radiation. A brief summary follows in Section 5. 2. OBSERVATIONS AND DATA REDUCTION The observations of HOPS 370 were performed as part of the Cycle 1 medium GO program \u201cInvestigating Protostellar Accretion (IPA),\u201d (PID 1802, Megeath et al. 2021), which carried out NIRSpec and MIRI IFU observations toward \ufb01ve protostars spanning \ufb01ve orders of magnitude in luminosity (see Federman et al. 2023). A set of 2 x 2 mosaics was obtained with NIRSpec using the G395M/F290LP disperser-\ufb01lter combination, which provides coverage of the 2.87 \u2013 5.10 \u00b5m spectral region at a spectral resolving power \u03bb/\u2206\u03bb \u223c1000, and with all channels of the MIRI/MRS to provide complete mid-infrared coverage from 4.9 to 27.9 \u00b5m at spectral resolving power that ranged from 1500 to 4000 (Jones et al. 2023). The mosaicking was performed with a 10% overlap and a 4-point dither pattern. The total observing time was about 7.5 hours, including overheads. Further details of the observing strategy have been presented by Narang et al. (2023) and Federman et al. (2023). For the reduction of NIRSpec IFU data, we utilized JWST pipeline version 1.9.5 and the JWST Calibration References Data System (CRDS) context version jwst 1069.pmap. In our analysis, we identi\ufb01ed hot pixels not captured by the JWST outlier detection step by applying a custom out5 lier detection algorithm speci\ufb01c to NIRSpec observations. More information on the NIRSpec data reduction and the custom \ufb02agging routine can be found in Federman et al. (2023). The MIRI MRS data reduction utilized JWST pipeline version 1.12.5 along with the JWST CRDS context version jwst 1179.pmap. We used the standard Stage 1 JWST pipeline Detector1Pipeline to reduce the MIRI MRS data starting from uncal data. In the subsequent Stage 2 (Spec2Pipeline), we performed pixel-by-pixel background subtraction using dedicated background observations. This process e\ufb00ectively removed all identi\ufb01ed bad pixels, resulting in background-subtracted cal products. However, we observed extended H2 S(1) and H2 S(2) emissions in the dedicated background observations, which led to reduced \ufb02ux for these lines in the \ufb01nal data. Consequently, we repeated the Spec2Pipeline without background subtraction. In this case, we encountered hot pixels in the detector data, which we removed using the VIP package (Gomez Gonzalez et al., 2017; Christiaens et al., 2023). Furthermore, we performed residual fringe correction during Stage 2 for both scenarios, with and without background subtraction. In Stage 3 (Spec3Pipeline), the CubeBuildStep was set to band mode, generating separate FITS \ufb01les for each channel and band. We also generated data cubes without dedicated background subtraction, with the outlier rejection function turned o\ufb00in these cases. We measured and applied an astrometric o\ufb00set calibration to the NIRSpec and MIRI IFU data to improve feature alignment and link the coordinates to the Gaia DR3 standard. The o\ufb00set measurement process and listed o\ufb00sets applied with uncertainties are presented in Federman et al. (2023). Additional data reduction tasks were performed using a suite of Python scripts we developed to (1) extract spectra within a circular region of any speci\ufb01ed position and radius; (2) \ufb01t and subtract a continuum from the extracted spectra; (3a) \ufb01t Gaussian lines to continuum-subtracted spectra obtained from task (2) above; or (3b) \ufb01t Gaussian lines with a \ufb01rst-order baseline at each IFU position and for each spectral line we targeted, thereby enabling us to generate spectral line maps. The second of these tasks (continuum \ufb01tting) was accomplished using a procedure that lacked any knowledge of the wavelengths of expected spectral lines. This \u201czero-knowledge\u201d feature avoids the risk of arti\ufb01cially creating spectral lines where lines are expected. Here, for each spectral channel, 6 we \ufb01t a third-order polynomial to the \ufb02uxes measured within a 17-channel window centered on that spectral channel (i.e. with 8 spectral channels on either side of the central one). The \ufb01t was optimized to achieve the best \ufb01t to any 10 of the 17 spectral channels in the window, and the continuum \ufb02ux value for the central channel was then assigned in accordance with that \ufb01t. For spectral regions where lines cover less than 7/17 \u223c40% of the spectral samples, this procedure yields a reliable separation of the continuum (including instrumental baseline ripples) from the lines. For the third task, Gaussian \ufb01tting, we used the Levenberg\u2013Marquardt algorithm; here, the line centroid and width were allowed to vary over a narrow range and the line intensity was allowed to vary freely, as were the continuum level and slope for task (3b). 3. RESULTS The IFU data acquired toward HOPS 370 are extraordinarily rich, revealing literally hundreds of spectral lines with a signal-to-noise ratio adequate for mapping. These data have and will be presented and discussed in series of papers, some already published (Federman et al. 2023; Rubinstein et al. 2023; Nazari et al. 2024; Brunken et al. 2024) and some in preparation. Here, we focus on the suprathermal OH lines and a small set of ancillary lines that are directly relevant to their interpretation. 3.1. Spectral line maps In Figure 1, we present maps of several spectral lines: a strong well-isolated water line within the \u03bd2 = 1 \u22120 vibrational band; the average of nine pure rotational lines of OH, with upper states with NU between 34 and 431; the Br\u03b1 line at 4.05 \u00b5m, which traces the Ly\u03b1 radiation responsible for the photodissociation of water to produce suprathermal OH emissions; the v = 0 \u22120 S(3) line of H2 at 9.66 \u00b5m, one of eight pure rotational lines detected with MIRI/MRS that may be used to estimate the extinction toward the source; the [Fe II] 5.34 \u00b5m line, a transition recently shown by Narang et al. (2023) to be an excellent tracer of collimated jets in another IPA target source, IRAS 16253-2429; 1 Here, we excluded the OH N = 37 \u221236 line, which lies very close to the much stronger S(3) line of H2 7 and the [Ne II] 12.81 \u00b5m line, a signature of fast, ionizing shocks. The maps are masked in the vicinity of a bright continuum source in the south, MIPS 2301 (Megeath et al. 2012), where the line \ufb01ts are unreliable. The RA and Dec o\ufb00sets are given in arcsec relative to the ALMA source position (T20, green star): RA = 83.865142 deg, Dec = \u20135.159561 deg (J2000). Red circles near the lower right of each panel indicate the half power beam width (HPBW) at the relevant wavelength, as determined by the linear \ufb01t given by Law et al. (2023). All these emissions peak roughly 0.8\u2032\u2032 north of the ALMA source position, near the location of the shocked knots identi\ufb01ed by Federman et al. (2023). The maps presented in Figure 1 exhibit a remarkable dynamic range: they are shown with a logarithmic stretch extending down to 0.1% of the peak intensity. In units of 10\u22124 erg cm\u22122 s\u22121sr\u22121, the peak velocity-integrated line intensities are 73, 1.14, 12.7, 36, 67, and 60 respectively for the H2O, OH, Br\u03b1, H2, [Fe II] and [Ne II] lines. For all the mapped lines other than the suprathermal OH emissions, a line is securely detected in every spaxel right up to the edges of the mapped region. While the [Fe II] and [Ne II] \ufb01ne structure emissions primarily trace a collimated bipolar jet, the H2 emissions are much less strongly collimated (Federman et al. 2023) and appear to trace a wide-angle wind. The Br\u03b1, OH and H2O emissions show an intermediate degree of collimation. Velocity shifts, although smaller than the instrumental linewidths, are clearly detected and indicate that the northern jet is tilted towards us and the southern jet away from us. They will be the subject of a future study. 3.2. OH suprathermal emission spectra In Figure 2, we present the 8.8 \u2013 13.4 \u00b5m spectra obtained toward the shocked knots within the circular region indicated by the white circle in Figure 1. This aperture has a radius of 0.8\u2032\u2032 and is centered at a projected distance of 316 au from the protostar (ALMA position) on the OH emission peak at o\ufb00set (\u2206\u03b1cos\u03b4, \u2206\u03b4) = (+0.1\u2032\u2032, +0.8\u2032\u2032). The spectral region shown in Figure 2 covers 24 securely-detected lines of OH, originating in states with NU ranging from 23 to 46, along with 5 \ufb01ne structure lines of [Ni II], [Co II], [Cl I] and [Ne II], and two pure rotational lines of H2, S(2) and S(3). 8 Figure 1. Spectral line maps obtained toward HOPS 370, shown with a logarithmic stretch. RA and Dec o\ufb00sets are given in arcsec relative to the ALMA source position (green star). The white circle demarks a 0.8\u2032\u2032 radius region centered on the shocked knot. The maps are masked near a bright continuum source in the south where the line \ufb01ts are unreliable. The red circles shown the beam size (HPBW). 9 Figure 2. 8.8 \u2013 13.4 \u00b5m spectra obtained toward the shocked knots. From top to bottom: Band 2B spectrum with continuum \ufb01t in blue; continuum-subtracted Band 2B, 2C, and 3A spectra. Red numbers above the OH lines indicate the value of NU. 10 From top to bottom, separate panels show the observed MIRI Band 2B (Channel 2 sub-band B) spectrum, with the continuum \ufb01t (blue) obtained using the procedure for task (2) described in Section 2 above; and the continuum-subtracted Band 2B, 2C, and 3A spectra. Colored vertical lines at the bottom of the lower three panels show the positions of suprathermal OH lines (Brooke et al. 2016), following the color coding indicated in the second panel from the top. Each rotational transition N \u2192N \u22121 is split into a quartet of lines by the combined e\ufb00ects of lambda-doubling and spin-orbit coupling, and the four lines are spectrally-resolvable by MIRI/MRS except at the highest values of N. Two of the four transitions connect so-called A\u2032 states, which are symmetric with respect to re\ufb02ection about the plane of rotation of the molecule, and two connect antisymmetric A\u2032\u2032 states. (A further hyper\ufb01ne splitting associated with the nuclear spin of H cannot be resolved spectrally with MIRI/MRS for any of the observed transitions.) The observed emission is completely dominated by intraladder transitions involving symmetric A\u2032 states of OH (i.e. the lower e lambda doublets of the 2\u03a03/2 ladder and the lower f lambda doublets of the 2\u03a01/2 ladder, shown with green and red lines.) In Figure 3, we show zoomed spectra of the suprathermal OH lines (yellow histogram). Here, the black lines show Gaussian \ufb01ts to each line. These were obtained with the central wavelengths allowed to vary over a narrow range but with the wavelength separation of the two components \ufb01xed at the laboratory value and the \ufb02ux ratio of the two components \ufb01xed at unity. The velocity scale is referenced to the average wavelength of the two components. At the spectral resolution of MIRI, the separation of the 2\u03a03/2(e) and 2\u03a01/2(f) transitions is unresolved for the highest-NU lines detected and fully-resolved for NU \u226423. Line positions are marked with vertical lines for each component of the OH quartet, with the same color-coding as in Figure 2: only the A\u2032 states (red and green) are detected. Some transitions with NU < 20 are detected, but most lie in spectral regions where \ufb02ux measurements are unreliable due to instrumental fringing. They are not plotted here, and their \ufb02uxes are not used in the analysis presented in Section 4.1 below. 11 Figure 3. Spectra of suprathermal OH lines observed toward the shocked knots. Yellow: observed spectrum. Line positions are marked with vertical lines for each component of the OH quartet, with the same color-coding as in Figure 2. Black histogram: Gaussian \ufb01t to the A\u2032 components (see text). 12 3.3. H2 rotational diagram and inferred extinction While the H2 emissions from HOPS 370 will be discussed in detail in a future publication, their present relevance is simply in providing a valuable extinction estimate. Their usefulness for this purpose arises because the S(3) line lies close to a local maximum in the extinction curve \u2013 associated with the silicate absorption feature \u2013 and therefore provides excellent leverage on the line-of-sight extinction. Using the intensities of the S(1) through S(8) pure rotational lines of H2, measured with MIRI/MRS, we constructed the rotational diagram shown in Figure 4. Here, we convolved the S(2) \u2013 S(8) MIRI maps with 2D-Gaussian kernels of the widths needed to degrade the spatial resolution to a common value for all lines. We then obtained average intensities for each line within the circular aperture indicated by the white circle in Figure 1. Following Neufeld et al. (2006), for example, we \ufb01t the rotational diagram with the sum of two components each in local thermodynamic equilibrium (LTE): a warm component at temperature Tw, with an aperture-averaged column density, Nw; and a hot component at temperature Th, with an aperture-averaged column density, Nh. These components were allowed to have separate ortho-topara ratios, OPRw and OPRh, yielding six free parameters to describe the rotational state of H2. The line-of-sight extinction was treated as a seventh free parameter that was adjusted, along with the other six, to optimize the \ufb01t (red and blue dashed curves). The best-\ufb01t values are indicated on Figure 4, and are typical of other protostellar out\ufb02ows observed with Spitzer (e.g. Neufeld et al. 2006). 2 2 The positive curvature of the rotational diagram, which we account for with a simple two-component model, suggests that a range of gas temperatures is present (although the temperature distribution need not be bimodal, e.g. Neufeld et al. 2009). The value of OPRw, lying signi\ufb01cantly below the value of 3 expected in LTE at temperature Tw, is suggestive of transient heating in a shock wave; here, the OPR retains a fossil record of its cooler preshock state, there having been insu\ufb03cient time for it to reach equilibrium (Neufeld et al. 2006, and references therein). 13 Figure 4. H2 rotational diagram obtained toward the shocked knots. Black points: no reddening correction. Blue and red points: reddening correction applied. Blue and red dashed lines: best \ufb01ts to the rotational diagram for ortho and para-H2. Following Narang et al. (2024), we adopted the KPv5 extinction curve (Pontoppidan et al. 2024) presented by Chapman et al. (2009), who cited a 2009 unpublished study by K. Pontoppidan for its origin and found that it provided the best \ufb01t to the mid-IR extinction and ice features observed in the Spitzer c2d program. The black points indicate the column densities in each rotational state inferred without any extinction correction, while the red and blue points show the values inferred from the extinction-corrected line \ufb02uxes. The best-\ufb01t extinction optical depth at 9.7\u00b5m is \u03c49.7 = 1.84, and other \ufb01tting parameters are speci\ufb01ed in Figure 4. To evaluate the sensitivity of our conclusions to our choice of extinction law and aperture size, we have also analysed the H2 rotational emissions within an aperture of radius 0.4\u2032\u2032 instead of 0.8\u2032\u2032 14 and for two additional mid-IR extinction laws that have appeared in the literature. The results are discussed in Appendix A, both as they pertain to the H2 analysis discussed above and to the OH analysis discussed below. The relative OH lines \ufb02uxes favor the KPv5 extinction curve over the alternative extinction laws considered in Appendix A, but the primary conclusions of our study are similar regardless of which mid-IR extinction law or aperture size we adopt. 4. DISCUSSION 4.1. Relative strengths of the suprathermal OH emission lines The high signal-to-noise ratio achieved in our observations of suprathermal OH emissions facilitates a demanding test of theoretical models for their origin. In Figure 5, we plot the mean photon intensity, extinction-corrected with the KPv5 extinction curve, as a function of NU (red crosses with bars showing the statistical errors). Here, we excluded the OH transitions with NU = 37, 28, and 25, which lie very close to the H2 S(3), [Cl I] 11.33 \u00b5m, and H2 S(2) lines, respectively. The results are in excellent agreement with the predictions presented in Appendix D of T21, which lists the number of OH line photons expected for each value of NU divided by the number of water photodissociations in the \u02dc B \u2212X band. These calculations, which rest upon theoretical calculations of the photodissociation dynamics (van Harrevelt & van Hemert 2000) and on experimental measurements (Harich et al. 2000), were presented by T21 for four di\ufb00erent radiation \ufb01elds. Those expected following water photodissociation by Ly\u03b1 radiation are shown by the blue curve. There is only one free parameter in this comparison: an overall vertical scaling that is proportional to the photodissociation rate within the beam. If every available UV photon led to a water photodissociation via the \u02dc B \u2212X band, the required UV photon intensity would be IUV = 1.67 \u00d7 109 photons cm\u22122 s\u22121sr\u22121. With 24 observed line intensities, the number of degrees of freedom here was Ndof = 23. Our analysis here is closely-related to that of T21. The only di\ufb00erence is that we present the minimum possible photon intensity, IUV, that would account for the absolute intensities of the observed OH emissions if every UV photon were absorbed locally by water. This photon intensity is a factor 15 4\u03c0 smaller than the quantity \u03a6 introduced by T21 and referred to there as the column density of H2O photodissociated per second. Figure 5. OH photon intensity as a function of NU. Red points: observed intensities. Also shown are the Tabone et al. (2021) predictions for H2O photodissociation by Ly\u03b1 radiation (blue) and by a 104 K blackbody (red). The observational intensities clearly show systematic errors that are not fully captured by the statistical error bars. Assuming (1) that the predicted curve for Ly\u03b1 photodissociation (blue) represents the true behavior, (2) that the statistical and systematic errors both have Gaussian distributions with dispersions that may be added in quadrature, and (3) that the fractional systematic error has the same r.m.s., \u01eb, for all lines, we adjusted \u01eb to achieve a reduced \u03c72 of unity for the best-\ufb01t scaling. The result was \u01eb = 0.105. 16 While the blue curve provides an excellent \ufb01t to the dependence of the line strengths on NU, one aspect of the T21 predictions is in con\ufb02ict with the observations. Whereas T21 predict roughly equal populations in the symmetric (2\u03a03/2(e) and 2\u03a01/2(f)) and antisymmetric states (2\u03a01/2(e) and 2\u03a03/2(f)) of OH, the observations indicate that the symmetric A\u2032 states are strongly favored; indeed, the antisymmetric A\u2032\u2032 states are not detected and are at least a factor \u223c10 less populated than the A\u2032 states. Regardless of the relative rates at which the symmetric and antisymmetric states are populated, the predictions presented in Appendix D of T21 are expected to apply to the total emission in all four NU \u2192NU \u22121 transitions (T21). This behavior, also noted in the recent paper of Zannese et al. (2023), is in fact entirely consistent with a recent theoretical study of the photodissociation process by Zhou et al. (2015), which indicates a population ratio A\u2032/A\u2032\u2032 \u223c40 at the Ly\u03b1 photon energy (their Figure 7). The astrophysical data thus provide a clear con\ufb01rmation of the molecular physics. A less-pronounced di\ufb00erence (\u223cfactor 2) between the line \ufb02uxes for the A\u2032 and A\u2032\u2032 transitions had previously been measured by Carr & Najita (2014) in Spitzer observations of the protostellar disk in DG Tau. These authors discussed the e\ufb00ect in detail, with reference to two possible origins for OH: photodissociation of H2O in the \u02dc B \u2212X band, and chemical pumping following formation via reaction of O(1D) with H2. The larger di\ufb00erence observed in HOPS 370 may indicate that chemical pumping is relatively less important in this source, at least for the NU \u226520 transitions discussed here. The NU-dependence of the OH line intensities provides information about the ultraviolet radiation \ufb01eld. The red curve in Figure 5 shows the predictions given by T21 (2021) for a blackbody radiation \ufb01eld at 104 K instead of a Ly\u03b1 radiation \ufb01eld. These tend to overpredict the \ufb02uxes for NU < 30 relative to those for NU > 40. For \u01eb = 0.105, the minimum reduced \u03c72 for this case is \u03c72 red = 2.98, implying that the blackbody radiation \ufb01eld is disfavored at the [Ndof(\u03c72 red\u22121)]1/2\u03c3 = 6.7\u03c3 signi\ufb01cance level. As we did for the H2 emissions discussed in Section 3.3, we have also analysed the OH emissions within an aperture of radius 0.4\u2032\u2032 instead of 0.8\u2032\u2032 and for two additional mid-IR extinction laws that have appeared in the literature. The results are discussed in Appendix A. 17 4.2. Fraction, fw, of Ly\u03b1 photons absorbed by water The number of Ly\u03b1 photons available to photodissociate water may be estimated from the Br\u03b1 \ufb02ux observed within the circular aperture centered on the shocked knots. In this analysis, we assume a geometry in which the Br\u03b1 and OH emissions are generated within the shocked knots and viewed directly rather than as a result of scattering, which is favored due their location in distinct shock knots. After degrading the resolution of the Br\u03b1 map to have the same HPBW as the OH lines, we obtain a value of 1.4 \u00d7 10\u221214 erg cm\u22122 s\u22121 for the Br\u03b1 \ufb02ux. If we apply an extinction correction assuming the value of \u03c49.7 obtained in Section 3.3 above, this corresponds to an intrinsic \ufb02ux of 3.3\u00d710\u221214 erg cm\u22122 s\u22121. As discussed in Appendix B, shock models appropriate for this source predict typical Ly\u03b1/Br\u03b1 luminosity ratios of \u223c900, a factor of several larger than the Case B recombination ratio because collisional excitation preferentially enhances Ly\u03b1. This would imply a Ly\u03b1 \ufb02ux within the aperture of 3.0 \u00d7 10\u221211 erg cm\u22122 s\u22121, or equivalently 1.8 photons cm\u22122 s\u22121. This corresponds to an aperture-averaged intensity of 3.8 \u00d7 1010 photons cm\u22122 s\u22121 sr\u22121, a factor of \u223c23 times as large as the minimum intensity of UV photons needed to account for the OH line \ufb02uxes (Section 4.1 above). Therefore, only a fraction fw = 4.3% of the available Ly\u03b1 photons would need to be absorbed by water to explain the OH emission. 4.3. Interpretation of fw Ly\u03b1 photons are unlikely to travel far without being absorbed by dust or water. For Ly\u03b1 radiation, we obtain a grain absorption cross-section per H nucleus of \u03c3abs(Ly\u03b1) = 1.9\u00d710\u221221 cm2, adopting the wavelength dependence and albedo given by KPv5; here, the overall scaling was chosen to match the average NH/AJ ratio of 5.6\u00d71021cm\u22122 mag\u22121 determined by Vuong et al. 2003 from X-ray absorption observations in several nearby dense clouds3. The water photodissociation cross-section for Ly\u03b1 is 1.53\u00d710\u221217 cm2 (Heays et al. 2017, and references therein), and thus the ratio of the water absorption rate to the grain absorption rate for Ly\u03b1 photons is R = 8\u00d7103 x(H2O), where x(H2O) = n(H2O)/nH 3 This scaling is also consistent with the standard NH/AV ratio in di\ufb00use molecular clouds (Bohlin et al. 1978), but yields a NH/AK ratio \u223c40% smaller than the average values determined toward diskless pre-main-sequence stars in Serpens and Orion by Winston et al. (2010) and Pillitteri et al. (2013) 18 is the water abundance relative to H nuclei. The corresponding fraction of Ly\u03b1 photons absorbed by water is fw = R/(1 + R). The estimate of R given above is critically dependent on the (poorly known) properties of grains in the out\ufb02ow. Indeed, it assumes that grains are present in protostellar out\ufb02ows \u2013 as suggested by Cacciapuoti et al. (2024) and references therein \u2013 and moreover that their properties are similar to those in the dense interstellar medium. The water abundance required to explain a given value of fw scales linearly with the adopted value of \u03c3abs(Ly\u03b1). If fw = 0.043 as determined in Section 4.2, and given the grain absorption cross-section assumed above, required water abundance is 5 \u00d7 10\u22126, amounting to only \u223c1% of the gas-phase oxygen abundance 4. This is the average value, \u00af x(H2O), encountered by the Ly\u03b1 photons as they su\ufb00er repeated scatterings with H atoms and execute a random walk prior to their eventual absorption. In the region of Ly\u03b1 production, the gas is warm (T > \u223c6000 K) and/or ionized and the water abundance will be extremely small. But if the photons escape the region where they are produced without being absorbed by dust, then the water abundance could plausibly exceed 10\u22124 if all oxygen nuclei were driven into gaseous water and R could exceed unity. In this scenario, the average water abundance is less meaningful, and the quantity fw might primarily re\ufb02ect the probability that a Ly\u03b1 photon escapes the warm region where it is originally generated and enters a region where water is abundant. The transfer of Ly\u03b1 radiation is a complex process (e.g. Neufeld 1990) that can be profoundly a\ufb00ected by velocity shifts associated with shock waves (Neufeld & McKee 1989). We defer a detailed treatment of this process to a future study. 4.4. Lower limit on the water abundance from H2O \u03bd2 = 1 \u22120 emissions The rovibrational water line map shown in the upper left panel of Figure 1 shows just one of several dozen emission lines detected in the H2O \u03bd2 = 1 \u22120 band, which collectively have a total equivalent width of \u223c0.120 \u00b5m. Figure 6 shows the 5.8 \u2013 7.0 spectral \u00b5m region that is dominated by these emission lines. Unless the density is extraordinarily high (nH > \u223c109 cm\u22123), these lines are too strong 4 As noted in Appendix B, our estimate of the required water abundance is quite strongly dependent upon the adopted grain properties: an alternative and widely-used grain model in the literature yields a value of only 1 \u00d7 10\u22126. 19 to be produced by collisional excitation. Colored symbols in Figure 6 show the line positions, with stars denoting transitions of ortho-water and crosses denoting those of para-water. A color code (top left) indicates the minimum energies, Emin, of the v = 0 states that must be pumped radiatively to excite each transition. We note here that Emin may be smaller than the energy, EL, of the lower state of the observed rovibrational transition, since radiative pumping via a given transition may be followed by radiative decay in a di\ufb00erent transition of longer wavelength. Roughly 90% of the water emission emerges in transitions that can be pumped radiatively out of the lowest 9 rotational states of water (i.e. those with J \u22642 and E/k < 160 K). This behavior suggests a low rotational temperature within H2O v = 0 state, most likely because the states are subthermally populated, and supports the hypothesis of radiative pumping. Although a full treatment of the H2O \u03bd2 = 1\u22120 emissions is beyond the scope of the present study, we may obtain a lower limit on the mean water abundance, x(H2O), by assuming that the observed lines are radiatively pumped by radiation from the protostar and that the observed continuum is radiation from the protostar that has been scattered by dust. The equivalent width of the water lines is then WH2O = X FH2O Fc \u2264 X R \u03c3\u03bb(H2O)d\u03bb \u03c3sca \u0012nl(H2O) nH \u0013 (1) where the sum is taken over all lines in the \u03bd2 = 1\u22120 band, WH2O = 0.120 \u00b5m is the total equivalent width (summed over all H2O lines), FH2O is the wavelength-integrated line \ufb02ux for a given line, Fc is the continuum \ufb02ux at the line wavelength, \u03c3sca is the grain scattering cross-section per H nucleus, nl(H2O) is the number density of water molecules in the lower state, and \u03c3\u03bb(H2O) is the H2O crosssection for a given rovibrational line (per molecule in the lower state), which has an integral over wavelength \u03bb given by Aul\u03bb4/(8\u03c0c), where Aul is the spontaneous radiative rate. The equality in equation (1) applies only if the pumping lines are optically-thin. 20 Figure 6. Average 5.8 \u2013 7.0 \u00b5m spectrum obtained toward the shocked knots, with rovibrational transitions of orthoand para-water marked with stars and crosses. Because the KPv5 grain model suggests that \u03c3sca varies only slowly over the band, we may take \u03c3sca as a constant and approximate the sum of Aul\u03bb4nl(H2O) as Aband\u00af \u03bb4n(H2O), where Aband = 24 s\u22121 is the total spontaneous radiation rate for the band and \u00af \u03bb = 6.3 \u00b5m is the average wavelength. Given the 21 grain scattering cross-section per H nucleus at 6.3 \u00b5m implied by KPv5, \u03c3sca(6.3) = 1.2\u00d710\u221223 cm\u22122, we then obtain5 x(H2O) = n(H2O) nH \u22658\u03c0c\u03c3sWH2O Aband\u00af \u03bb4 = 3 \u00d7 10\u22125. (2) Our water abundance of 3\u00d710\u22125 is a lower limit, and \u2013 depending on the water linewidths \u2013 would likely increase if optical depth e\ufb00ects are included. But even this minimum estimate is a factor 6 larger than the value needed to yield the inferred value of fw (Section 4.3 above). This supports a picture in which most Ly\u03b1 photons are absorbed by dust in a warm and/or ionized zone very close to where they are created in a fast shock and only a minority escape to the region of signi\ufb01cant water abundance that is probed by the water rovibrational emissions. Like the estimate of \u00af x(H2O) derived in section 4.3 above, this independent estimate of the minimum water abundance, derived from WH2O, is also dependent on the grain properties in the out\ufb02ow; it scales linearly with the value adopted for \u03c3sca(6.3). If grains were depleted in the out\ufb02ow (while maintaining the ratio of \u03c3sca(6.3) to \u03c3abs(Ly\u03b1)), both water abundance estimates would decrease proportionally. Future detailed analyses of the H2O \u03bd2 = 1\u22120 spectrum and how it varies spatially will be needed to discriminate between the various mechanisms that release water from ices into the gas-phase: these include thermal desorption, sputtering in shocks, and UV photodesorption. 5. SUMMARY We have presented a study of OH in an out\ufb02ow jet from the HOPS 370 protostar observed with MIRI and NIRSpec as part of the IPA program. 1. We have detected pure rotational, suprathermal OH emissions from the vicinity of the intermediate-mass protostar HOPS 370 (OMC2/FIR3). These emissions are observed from shocked knots in a jet/out\ufb02ow, and originate in states of rotational quantum number as high as 46 that possess excitation energies as large as EU/k = 4.65 \u00d7 104 K. Only symmetric A\u2032 states of OH are observed. 5 A similar argument can be used to determine the CO abundance from observations (Rubinstein et al. 2023) of the CO v = 1 \u22120 band: here, we obtain a total equivalent width of 0.140 \u00b5m which implies a minimum CO abundance of 1.1 \u00d7 10\u22124 relative to H nuclei. 22 2. The relative OH line strengths are entirely consistent with a picture in which the suprathermal OH states are populated following the photodissociation of water in its \u02dc B \u2212X band by Ly\u03b1 radiation produced locally be a fast, ionizing shock. Photodissociation by a blackbody radiation \ufb01eld at 104 K is found to provide a signi\ufb01cantly worse \ufb01t to the relative OH line strengths. 3. Using measurements of the Br\u03b1 \ufb02ux to estimate the Ly\u03b1 production rate in shocked gas near HOPS 370, we \ufb01nd that \u223c4% of the Ly\u03b1 photons are absorbed by water. 4. The fraction of Ly\u03b1 photons absorbed by water implies a mean water abundance (relative to H nuclei) in the range \u00af x(H2O) \u223c1 \u22125 \u00d7 10\u22126, the derived value depending upon the adopted grain properties (Appendix B). This estimate is proportional to the grain absorption cross-section assumed at the Ly\u03b1 wavelength (121.6 nm), and represents the average abundance within the region where Ly\u03b1 photons scatter prior to being absorbed by dust or water. 5. Assuming that the H2O \u03bd2 band emissions observed from HOPS 370 are radiatively-pumped and that the continuum is scattered light, we obtain a minimum water abundance in the range xmin = 0.7 \u22123 \u00d710\u22125, the derived value depending upon the adopted grain properties (Appendix A). This minimum value is proportional to the grain scattering cross-section assumed at 6 \u00b5m, and would be exceeded if the pumping lines are optically-thick. It is a factor of several larger than \u00af x(H2O), suggesting that most Ly\u03b1 photons are absorbed by dust in a warm and/or ionized zone very close to where they are created in a fast shock and that only a minority escape to the region of signi\ufb01cant water abundance that emits the water rovibrational emissions we observe. 6. Suprathermal OH emissions promise to help elucidate the processes whereby Lyman \u03b1 radiation \ufb01rst escapes from fast shocks and then enters nearby water-rich surroundings where water has been released from grain mantles by radiative heating or slower non-dissociative shocks, or produced in the gas-phase by neutral-neutral reactions that are slow at low temperatures but rapid at the elevated temperatures attained behind shock fronts. Detailed models, beyond the scope of this Letter, will be needed to understand the transfer of Ly\u03b1 radiation and to fully model the rovibrational water emissions observed from HOPS 370. 23 ACKNOWLEDGMENTS We thank the referee, Beno\u02c6 \u0131t Tabone, for a very detailed and helpful review containing multiple suggestions that improved this paper. This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with program #1802. D.A.N. was supported by grant SOF08-0038 from USRA. P.M. and H.T. acknowledge support of the Department of Atomic Energy, Government of India, under Project Identi\ufb01cation No. RTI 4002. Support for S.F., A.E.R., S.T.M., R.G., W.F., J.G., J.J.T. and D.W. in program #1802 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127. A.C.G. has been supported by PRIN-MUR 2022 20228JPA3A \u201cThe path to star and planet formation in the JWST era (PATH)\u201d and by INAF-GoG 2022 \u201cNIR-dark Accretion Outbursts in Massive Young stellar objects (NAOMY)\u201d. G.A. and M.O., acknowledge \ufb01nancial support from grants PID2020-114461GB-I00 and CEX2021-001131S, funded by MCIN/AEI/10.13039/501100011033. Y.L.Y. acknowledges support from Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (20H05845, 20H05844, 22K20389), and a pioneering project in RIKEN (Evolution of Matter in the Universe). W.R.M.R. is grateful for support from the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programme (grant agreement No. 101019751 MOLDISK). All the data presented in this article were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The speci\ufb01c observations analyzed can be accessed via 10.17909/3kky-t040 24 APPENDIX A. DEPENDENCE ON ADOPTED EXTINCTION CURVE AND APERTURE SIZE We have evaluated the sensitivity of our conclusions to our choice of extinction law and aperture size. Results are presented in Table 1 for six cases. We considered three di\ufb00erent extinction curves \u2013 denoted KP (KPv5), WD (Weingartner and Draine, 2001, with the modi\ufb01cations described in Draine 2003); and MM (McClure 2009) \u2013 and two di\ufb00erent aperture radii (0.8\u2032\u2032 and 0.4\u2032\u2032, denoted by 1 and 2). The standard model, adopted in the main text, is KP1 (KPv5 extinction curve with the 0.8\u2032\u2032 radius aperture). Di\ufb00erent rows in Table 1 show the values obtained for key parameters for all six cases. The \ufb01rst row below the horizontal line lists the optical depth at 9.7 \u00b5m, \u03c49.7, derived from our \ufb01t to the H2 lines. It ranges from 1.53 to 3.12, with the MM extinction law (which is signi\ufb01cantly less dominated by the silicate peak) requiring the largest \u03c49.7 and the WD extinction law requiring the smallest, but shows very little variation with the adopted aperture size. The second row lists, IUV , the required UV photon intensity if every available UV photon led to a water photodissociation via the \u02dc B \u2212X band. In determining IUV , the OH lines were extinction-corrected using the speci\ufb01ed extinction curve and the corresponding value of \u03c49.7, and Ly\u03b1 was assumed to be responsible for water photodissociation. As discussed in Section 4.1, we assumed equal fractional systematic errors, \u01eb, for each OH \ufb02ux measurement and adjusted \u01eb to yield a reduced \u03c72 of unity when comparing case KP1 and KP2 \ufb02uxes with the predictions for Ly\u03b1 photodissociation. The third row lists the reduced \u03c72 obtained for each of the six cases. The fourth row lists the corresponding values obtained for a 104 K blackbody radiation \ufb01eld instead of Ly\u03b1. The \ufb01fth and sixth rows indicate the signi\ufb01cance with which each case is disfavored relative to KP1 or KP2 with photodissociation by Ly\u03b1. The values plotted here indicate (1) that the KP extinction law yields a signi\ufb01cantly better \ufb01t to the data than either WD or MM; (2) for any extinction curve, assuming photodissociation by Ly\u03b1 radiation yields a signi\ufb01cantly better \ufb01t to the data than does assuming photodissociation by a 104 blackbody. 25 The seventh row in Table 1 lists the extinction-corrected (ec) Br\u03b1 intensity, I(Br\u03b1)ec for each of the six cases. The next row lists the corresponding values of fw, the fraction of Ly\u03b1 photons absorbed by dust. The quantity fw was computed for an assumed Ly\u03b1/Br\u03b1 ratio of 900 (see Appendix B) and is proportional to IUV /I(Br\u03b1)ec. Although IUV varies over a factor of 4 \u2013 5 as di\ufb00erent extinction curves are adopted, fw varies by less than a factor 2. This is because there is some degree of cancellation between the e\ufb00ects on IUV and I(Br\u03b1)ec. The MM extinction curve, for example, requires a signi\ufb01cantly larger \u03c49.7 leading to a signi\ufb01cantly larger IUV : but because the opacity is less strongly peaked at silicate feature, I(Br\u03b1)ec also increases by a factor 2. The conclusions of our sensitivity analysis are (1) similar results are obtained for both aperture sizes; (2) as the origin of the suprathermal OH emissions, water photodissociation by Ly\u03b1 radiation is robustly favored over photodissociation by a 104 K blackbody; (3) the KPv5 extinction is favored over the other two extinction laws considered here; and (4) the parameter fw lies in the range 2.6 4.3 % for any of the extinction laws we considered. Rows 9 13 are relevant to the water abundances discussed in Sections 4.3 and 4.4. Here, not only is the relative extinction at di\ufb00erent wavelengths of relevance, but so too is the grain albedo and the ratio of extinction to column density, NH. Both these parameters are available for the KP and WD extinction laws but not for MM. Row 9 lists the grain absorption cross-section per H nucleus, \u03c3abs(Ly\u03b1), given by each extinction law. The average water abundance, \u00af x(H2O), needed to account for fw is listed in Row 10 (see Section 4.3). Row 11 lists the grain scattering cross-section, \u03c3sca(6.3), needed for the analysis presented in Section 4.4, while Row 12 lists the total \u03bd2 = 1 \u22120 equivalent width, WH2O, for each aperture. The resultant minimum water abundances, xmin(H2O) (see Section 4.3), are given in Row 13. The results presented here for \u00af x(H2O) and xmin(H2O) are clearly more sensitive to uncertainties in the dust properties. Nevertheless, the conclusion that \u00af x(H2O) < xmin(H2O) appears to be robust, with the implications for Ly\u03b1 radiative transfer discussed in Section 4.4. 26 Table 1. Results for di\ufb00erent extinction laws and aperture sizes Row Quantity KP1 WD1 MM1 KP2 WD2 MM2 0.8\u2032\u2032 0.8\u2032\u2032 0.8\u2032\u2032 0.4\u2032\u2032 0.4\u2032\u2032 0.4\u2032\u2032 1 \u03c49.7 1.84 1.53 3.12 1.85 1.53 3.05 2 IUV (109 photons cm\u22122 s\u22121 sr\u22121) 1.67 1.10 5.11 3.75 2.42 1.07 3 Reduced \u03c72 (w.r.t. Ly\u03b1 model) 1.00 1.63 1.55 1.00 2.65 2.33 4 Reduced \u03c72 (w.r.t. 104 K BB model) 2.98 6.13 4.60 3.74 8.40 7.30 5 Signi\ufb01cancea (for Ly\u03b1 model) 0.0\u03c3 4.4\u03c3 3.6\u03c3 0.0\u03c3 6.2\u03c3 5.5\u03c3 6 Signi\ufb01cancea (for 104 K BB model) 6.7\u03c3 10.9\u03c3 9.1\u03c3 7.9\u03c3 13.0\u03c3 12.0\u03c3 7 I(Br\u03b1)ec (10\u22123 erg cm\u22122 s\u22121 sr\u22121) 0.71 0.72 3.64 1.49 1.52 7.22 8 fw 0.043 0.028 0.025 0.046 0.029 0.027 9 \u03c3abs(Ly\u03b1) (10\u221221 cm2) 1.73 0.70 N/A 1.73 0.70 N/A 10 \u00af x(H2O) 5.1 \u00d7 10\u22126 1.3 \u00d7 10\u22126 N/A 5.1 \u00d7 10\u22126 1.3 \u00d7 10\u22126 N/A 11 \u03c3sca(6.3) (10\u221223 cm2) 1.26 0.29 N/A 1.26 0.29 N/A 12 WH2O (\u00b5m) 0.120 0.120 0.120 0.168 0.168 0.168 13 xmin(H2O) 3.0 \u00d7 10\u22125 7.0 \u00d7 10\u22126 N/A 4.2 \u00d7 10\u22125 1.0 \u00d7 10\u22125 N/A aSigni\ufb01cance with which a given model and extinction curve is disfavored relative to the model with Ly\u03b1 photodissociation and the KP extinction curve. B. SHOCK MODEL PREDICTIONS FOR Ly\u03b1/Br\u03b1 We have used publicly-available the MAPPINGS V shock model (Sutherland & Dopita 2017; Sutherland et al. 2018) to estimate the Ly\u03b1/Br\u03b1 luminosity ratio within the shocked region where suprathermal OH emissions were detected. The upper states of these lines may be populated both following recombination of H+ and by direct colllisional excitation of neutral hydrogen from the ground state. The Ly\u03b1/Br\u03b1 ratio can signi\ufb01cantly exceed the Case B recombination value \u223c300, particularly for lower velocity shocks where collisional excitation is most important, so the use of shock model predictions is important here. We ran a grid of models with preshock densities, n0, spanning the range 10\u22121 to 105.5 H nuclei per cm\u22123 in steps of 0.1 dex; and with shock velocities, vs, spanning the range 30 to 220 km s\u22121 in steps 27 of 5 km s\u22121. The preshock ionization state was determined self-consistently. The preshock magnetic \ufb01eld was taken as 0.5 (n0/cm\u22123)1/2 \u00b5G, and undepleted solar abundances were adopted. The collision strengths for [Fe II] \ufb01ne structure transitions were updated to the values given in the recent study of Tayal & Zatsarinny (2018). Figure 7 shows contours of the predicted Ly\u03b1/Br\u03b1 luminosity ratio in the plane of vs and log10n0. Here, the red, cyan and blue contours show where the Ly\u03b1/Br\u03b1 ratio is predicted to be 1000, 1500, and 2000, and black contours show intermediate values spaced by 100. The [Ne III] 15.6 \u00b5m to [Ne II] 12.8 \u00b5m \ufb02ux ratio is an excellent tracer of shock velocity. The observed, extinction-corrected value of 0.026 is obtained for shock parameters lying along the locus marked with the green solid curve. The green band indicates the region where the predicted value lies within a factor 1.5 of that observed, with the dotted/dashed boundaries applying to larger/smaller line ratios. As a probe of the preshock density, we have considered the [Fe II] 17.9 \u00b5m to [Fe II] 5.3 \u00b5m \ufb02ux ratio, which has an observed extinction-corrected value of 4.17. The magenta curves and magenta band represent analogous results for the [Fe II] line ratio. The constraint on density is less tight, as indicated by the width of the magenta band, and must be considered less reliable because recent independent estimates of the collision strengths show signi\ufb01cant di\ufb00erences. Nevertheless, the intersection of the green and magenta solid lines suggest that Ly\u03b1/Br\u03b1 ratio of 900 is consistent with these diagnostic line ratios. For any preshock density in the range 102 to 105 cm\u22123, the \ufb02ux [Ne III] 15.6 \u00b5m to [Ne II] 12.8 \u00b5m \ufb02ux ratio alone suggests a Ly\u03b1/Br\u03b1 ratio in range 700 \u2013 1050. 28 Figure 7. Contours of the predicted Ly\u03b1/Br\u03b1 luminosity ratio in the plane of vs and log10n0. Red, cyan and blue contours: Ly\u03b1/Br\u03b1 = 1000, 1500, and 2000. Green band: region where the predicted [Ne III] 15.6 \u00b5m to [Ne II] 12.8 \u00b5m \ufb02ux ratio lies within a factor 1.5 of that observed. Magenta band: region where the predicted [Fe II] 17.94 \u00b5m to [Fe II] 5.34 \u00b5m \ufb02ux ratio lies within a factor 1.5 of that observed. 29"
+        }
+    ]
+}
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